[PATCH 2/8] math-emu: Import current glibc soft-fp as include/math-emu

From: Joseph Myers
Date: Thu Jul 02 2015 - 11:48:06 EST

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From: Joseph Myers <joseph@xxxxxxxxxxxxxxxx>

The include/math-emu code having been moved to math-emu-old, this
patch imports the current glibc soft-fp code as include/math-emu
(verbatim).

The following changes have occurred in the soft-fp API since the
version used in the kernel and so are addressed in the architecture
updates in subsequent patches that move each architecture from
math-emu-old to math-emu. (This list only includes changes relating
to features used in the kernel, not pure new features that aren't
relevant to updating existing code, and not pure bug fixes.)

* <https://sourceware.org/ml/libc-alpha/2006-02/msg00028.html>

- Semi-raw unpacking is added, as something intermediate between raw
and cooked unpacking, for efficiency.

- Addition and subtraction are changed to work on semi-raw values.
Thus, cooked results of multiplication can't be passed directly
into addition, as was done in some kernel emulations of fused
multiply-add, but that isn't a proper fused operation anyway (a
proper fused operation involves using the unrounded multiplication
result in twice the input precision, not an intermediate value in
input precision plus three working bits); the appropriate fix is
to use the new fused multiply-add support in soft-fp.

- Conversions from one floating-point type to another now use
FP_EXTEND (raw) and FP_TRUNC (semi-raw) instead of FP_CONV
(cooked). Those operations now deal with quieting signaling NaNs.

- Conversions from floating-point to integer now use raw inputs, and
require the integer variable passed to the FP_TO_INT macros to
have unsigned type.

- Conversions from integer to floating-point now use raw outputs.

* <https://sourceware.org/ml/libc-alpha/2006-02/msg00044.html>

- Conversions from integer to floating-point now pass the name of an
unsigned type to the FP_FROM_INT macros, not a signed type to
which "unsigned" is added in the macro definition.

* <https://sourceware.org/ml/libc-alpha/2013-04/msg00646.html>

- soft-fp supports the reversed quiet NaN convention used on MIPS
and HPPA; sfp-machine.h must define _FP_QNANNEGATEDP (to 0, for
architectures using the normal convention; to 1, for architectures
using the MIPS convention).

* <https://sourceware.org/ml/libc-alpha/2013-10/msg00348.html>

- Negation now works on raw values.

* <https://sourceware.org/ml/libc-alpha/2014-02/msg00068.html>

- soft-fp now supports after-rounding tininess detection for
architectures where that is the defined way in which tiny results
are detected (of the architectures for which the Linux kernel uses
this code, that's Alpha and SH). sfp-machine.h must define
_FP_TININESS_AFTER_ROUNDING to either 0 or 1.

* <https://sourceware.org/ml/libc-alpha/2014-09/msg00411.html>

- FP_CLEAR_EXCEPTIONS is removed; all uses in the Linux kernel are
no longer needed as, now unpacking only occurs in the correct
format, exceptions are already clear at that point.

* <https://sourceware.org/ml/libc-alpha/2014-09/msg00461.html>

- The FP_CMP macros have an extra argument to specify when
exceptions should be set (0 for no exception setting, 1 for
exceptions only for signaling NaNs, 2 for exceptions for all
NaNs). In the old version in the kernel, it was necessary for the
caller to handle all exception setting for comparisons.

* <https://sourceware.org/ml/libc-alpha/2014-09/msg00488.html>

- FP_DENORM_ZERO does not set "inexact" when flushing to zero, as
that does not appear to match the documented semantics for either
of the architectures (Alpha and SH) for which the kernel uses
FP_DENORM_ZERO. FP_DENORM_ZERO is also checked for comparisons
(the documentation for both Alpha and SH is explicit that their
corresponding control bits do apply to comparisons).

* <https://sourceware.org/ml/libc-alpha/2014-09/msg00462.html>

- The more precise FP_EX_INVALID_* exceptions include more cases
than in the kernel version (in particular, FP_EX_INVALID_IMZ_FMA
is split out from FP_EX_INVALID_IMZ, so if only the latter is
defined then fma using the new fma support would not raise that
exception any more - except that this doesn't actually affect
powerpc because it hardcodes setting various exceptions in
powerpc-specific code despite also defining FP_EX_INVALID_*).

Signed-off-by: Joseph Myers <joseph@xxxxxxxxxxxxxxxx>

---

diff --git a/include/math-emu/double.h b/include/math-emu/double.h
new file mode 100644
index 0000000..a05713f
--- /dev/null
+++ b/include/math-emu/double.h
@@ -0,0 +1,323 @@
+/* Software floating-point emulation.
+ Definitions for IEEE Double Precision
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_DOUBLE_H
+#define SOFT_FP_DOUBLE_H 1
+
+#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_D (2 * _FP_W_TYPE_SIZE)
+# define _FP_FRACTBITS_DW_D (4 * _FP_W_TYPE_SIZE)
+#else
+# define _FP_FRACTBITS_D _FP_W_TYPE_SIZE
+# define _FP_FRACTBITS_DW_D (2 * _FP_W_TYPE_SIZE)
+#endif
+
+#define _FP_FRACBITS_D 53
+#define _FP_FRACXBITS_D (_FP_FRACTBITS_D - _FP_FRACBITS_D)
+#define _FP_WFRACBITS_D (_FP_WORKBITS + _FP_FRACBITS_D)
+#define _FP_WFRACXBITS_D (_FP_FRACTBITS_D - _FP_WFRACBITS_D)
+#define _FP_EXPBITS_D 11
+#define _FP_EXPBIAS_D 1023
+#define _FP_EXPMAX_D 2047
+
+#define _FP_QNANBIT_D \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_D-2) % _FP_W_TYPE_SIZE)
+#define _FP_QNANBIT_SH_D \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_D-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
+#define _FP_IMPLBIT_D \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_D-1) % _FP_W_TYPE_SIZE)
+#define _FP_IMPLBIT_SH_D \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_D-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
+#define _FP_OVERFLOW_D \
+ ((_FP_W_TYPE) 1 << _FP_WFRACBITS_D % _FP_W_TYPE_SIZE)
+
+#define _FP_WFRACBITS_DW_D (2 * _FP_WFRACBITS_D)
+#define _FP_WFRACXBITS_DW_D (_FP_FRACTBITS_DW_D - _FP_WFRACBITS_DW_D)
+#define _FP_HIGHBIT_DW_D \
+ ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_D - 1) % _FP_W_TYPE_SIZE)
+
+typedef float DFtype __attribute__ ((mode (DF)));
+
+#if _FP_W_TYPE_SIZE < 64
+
+union _FP_UNION_D
+{
+ DFtype flt;
+ struct _FP_STRUCT_LAYOUT
+ {
+# if __BYTE_ORDER == __BIG_ENDIAN
+ unsigned sign : 1;
+ unsigned exp : _FP_EXPBITS_D;
+ unsigned frac1 : _FP_FRACBITS_D - (_FP_IMPLBIT_D != 0) - _FP_W_TYPE_SIZE;
+ unsigned frac0 : _FP_W_TYPE_SIZE;
+# else
+ unsigned frac0 : _FP_W_TYPE_SIZE;
+ unsigned frac1 : _FP_FRACBITS_D - (_FP_IMPLBIT_D != 0) - _FP_W_TYPE_SIZE;
+ unsigned exp : _FP_EXPBITS_D;
+ unsigned sign : 1;
+# endif
+ } bits __attribute__ ((packed));
+};
+
+# define FP_DECL_D(X) _FP_DECL (2, X)
+# define FP_UNPACK_RAW_D(X, val) _FP_UNPACK_RAW_2 (D, X, (val))
+# define FP_UNPACK_RAW_DP(X, val) _FP_UNPACK_RAW_2_P (D, X, (val))
+# define FP_PACK_RAW_D(val, X) _FP_PACK_RAW_2 (D, (val), X)
+# define FP_PACK_RAW_DP(val, X) \
+ do \
+ { \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_2_P (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_D(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2 (D, X, (val)); \
+ _FP_UNPACK_CANONICAL (D, 2, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_DP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2_P (D, X, (val)); \
+ _FP_UNPACK_CANONICAL (D, 2, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_D(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2 (D, X, (val)); \
+ _FP_UNPACK_SEMIRAW (D, 2, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_DP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2_P (D, X, (val)); \
+ _FP_UNPACK_SEMIRAW (D, 2, X); \
+ } \
+ while (0)
+
+# define FP_PACK_D(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (D, 2, X); \
+ _FP_PACK_RAW_2 (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_DP(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (D, 2, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_2_P (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_D(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (D, 2, X); \
+ _FP_PACK_RAW_2 (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_DP(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (D, 2, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_2_P (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_ISSIGNAN_D(X) _FP_ISSIGNAN (D, 2, X)
+# define FP_NEG_D(R, X) _FP_NEG (D, 2, R, X)
+# define FP_ADD_D(R, X, Y) _FP_ADD (D, 2, R, X, Y)
+# define FP_SUB_D(R, X, Y) _FP_SUB (D, 2, R, X, Y)
+# define FP_MUL_D(R, X, Y) _FP_MUL (D, 2, R, X, Y)
+# define FP_DIV_D(R, X, Y) _FP_DIV (D, 2, R, X, Y)
+# define FP_SQRT_D(R, X) _FP_SQRT (D, 2, R, X)
+# define _FP_SQRT_MEAT_D(R, S, T, X, Q) _FP_SQRT_MEAT_2 (R, S, T, X, (Q))
+# define FP_FMA_D(R, X, Y, Z) _FP_FMA (D, 2, 4, R, X, Y, Z)
+
+# define FP_CMP_D(r, X, Y, un, ex) _FP_CMP (D, 2, (r), X, Y, (un), (ex))
+# define FP_CMP_EQ_D(r, X, Y, ex) _FP_CMP_EQ (D, 2, (r), X, Y, (ex))
+# define FP_CMP_UNORD_D(r, X, Y, ex) _FP_CMP_UNORD (D, 2, (r), X, Y, (ex))
+
+# define FP_TO_INT_D(r, X, rsz, rsg) _FP_TO_INT (D, 2, (r), X, (rsz), (rsg))
+# define FP_TO_INT_ROUND_D(r, X, rsz, rsg) \
+ _FP_TO_INT_ROUND (D, 2, (r), X, (rsz), (rsg))
+# define FP_FROM_INT_D(X, r, rs, rt) _FP_FROM_INT (D, 2, X, (r), (rs), rt)
+
+# define _FP_FRAC_HIGH_D(X) _FP_FRAC_HIGH_2 (X)
+# define _FP_FRAC_HIGH_RAW_D(X) _FP_FRAC_HIGH_2 (X)
+
+# define _FP_FRAC_HIGH_DW_D(X) _FP_FRAC_HIGH_4 (X)
+
+#else
+
+union _FP_UNION_D
+{
+ DFtype flt;
+ struct _FP_STRUCT_LAYOUT
+ {
+# if __BYTE_ORDER == __BIG_ENDIAN
+ unsigned sign : 1;
+ unsigned exp : _FP_EXPBITS_D;
+ _FP_W_TYPE frac : _FP_FRACBITS_D - (_FP_IMPLBIT_D != 0);
+# else
+ _FP_W_TYPE frac : _FP_FRACBITS_D - (_FP_IMPLBIT_D != 0);
+ unsigned exp : _FP_EXPBITS_D;
+ unsigned sign : 1;
+# endif
+ } bits __attribute__ ((packed));
+};
+
+# define FP_DECL_D(X) _FP_DECL (1, X)
+# define FP_UNPACK_RAW_D(X, val) _FP_UNPACK_RAW_1 (D, X, (val))
+# define FP_UNPACK_RAW_DP(X, val) _FP_UNPACK_RAW_1_P (D, X, (val))
+# define FP_PACK_RAW_D(val, X) _FP_PACK_RAW_1 (D, (val), X)
+# define FP_PACK_RAW_DP(val, X) \
+ do \
+ { \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_1_P (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_D(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1 (D, X, (val)); \
+ _FP_UNPACK_CANONICAL (D, 1, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_DP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1_P (D, X, (val)); \
+ _FP_UNPACK_CANONICAL (D, 1, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_D(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1 (D, X, (val)); \
+ _FP_UNPACK_SEMIRAW (D, 1, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_DP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1_P (D, X, (val)); \
+ _FP_UNPACK_SEMIRAW (D, 1, X); \
+ } \
+ while (0)
+
+# define FP_PACK_D(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (D, 1, X); \
+ _FP_PACK_RAW_1 (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_DP(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (D, 1, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_1_P (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_D(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (D, 1, X); \
+ _FP_PACK_RAW_1 (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_DP(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (D, 1, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_1_P (D, (val), X); \
+ } \
+ while (0)
+
+# define FP_ISSIGNAN_D(X) _FP_ISSIGNAN (D, 1, X)
+# define FP_NEG_D(R, X) _FP_NEG (D, 1, R, X)
+# define FP_ADD_D(R, X, Y) _FP_ADD (D, 1, R, X, Y)
+# define FP_SUB_D(R, X, Y) _FP_SUB (D, 1, R, X, Y)
+# define FP_MUL_D(R, X, Y) _FP_MUL (D, 1, R, X, Y)
+# define FP_DIV_D(R, X, Y) _FP_DIV (D, 1, R, X, Y)
+# define FP_SQRT_D(R, X) _FP_SQRT (D, 1, R, X)
+# define _FP_SQRT_MEAT_D(R, S, T, X, Q) _FP_SQRT_MEAT_1 (R, S, T, X, (Q))
+# define FP_FMA_D(R, X, Y, Z) _FP_FMA (D, 1, 2, R, X, Y, Z)
+
+/* The implementation of _FP_MUL_D and _FP_DIV_D should be chosen by
+ the target machine. */
+
+# define FP_CMP_D(r, X, Y, un, ex) _FP_CMP (D, 1, (r), X, Y, (un), (ex))
+# define FP_CMP_EQ_D(r, X, Y, ex) _FP_CMP_EQ (D, 1, (r), X, Y, (ex))
+# define FP_CMP_UNORD_D(r, X, Y, ex) _FP_CMP_UNORD (D, 1, (r), X, Y, (ex))
+
+# define FP_TO_INT_D(r, X, rsz, rsg) _FP_TO_INT (D, 1, (r), X, (rsz), (rsg))
+# define FP_TO_INT_ROUND_D(r, X, rsz, rsg) \
+ _FP_TO_INT_ROUND (D, 1, (r), X, (rsz), (rsg))
+# define FP_FROM_INT_D(X, r, rs, rt) _FP_FROM_INT (D, 1, X, (r), (rs), rt)
+
+# define _FP_FRAC_HIGH_D(X) _FP_FRAC_HIGH_1 (X)
+# define _FP_FRAC_HIGH_RAW_D(X) _FP_FRAC_HIGH_1 (X)
+
+# define _FP_FRAC_HIGH_DW_D(X) _FP_FRAC_HIGH_2 (X)
+
+#endif /* W_TYPE_SIZE < 64 */
+
+#endif /* !SOFT_FP_DOUBLE_H */
diff --git a/include/math-emu/op-1.h b/include/math-emu/op-1.h
new file mode 100644
index 0000000..e3a91bf
--- /dev/null
+++ b/include/math-emu/op-1.h
@@ -0,0 +1,369 @@
+/* Software floating-point emulation.
+ Basic one-word fraction declaration and manipulation.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_OP_1_H
+#define SOFT_FP_OP_1_H 1
+
+#define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f _FP_ZERO_INIT
+#define _FP_FRAC_COPY_1(D, S) (D##_f = S##_f)
+#define _FP_FRAC_SET_1(X, I) (X##_f = I)
+#define _FP_FRAC_HIGH_1(X) (X##_f)
+#define _FP_FRAC_LOW_1(X) (X##_f)
+#define _FP_FRAC_WORD_1(X, w) (X##_f)
+
+#define _FP_FRAC_ADDI_1(X, I) (X##_f += I)
+#define _FP_FRAC_SLL_1(X, N) \
+ do \
+ { \
+ if (__builtin_constant_p (N) && (N) == 1) \
+ X##_f += X##_f; \
+ else \
+ X##_f <<= (N); \
+ } \
+ while (0)
+#define _FP_FRAC_SRL_1(X, N) (X##_f >>= N)
+
+/* Right shift with sticky-lsb. */
+#define _FP_FRAC_SRST_1(X, S, N, sz) __FP_FRAC_SRST_1 (X##_f, S, (N), (sz))
+#define _FP_FRAC_SRS_1(X, N, sz) __FP_FRAC_SRS_1 (X##_f, (N), (sz))
+
+#define __FP_FRAC_SRST_1(X, S, N, sz) \
+ do \
+ { \
+ S = (__builtin_constant_p (N) && (N) == 1 \
+ ? X & 1 \
+ : (X << (_FP_W_TYPE_SIZE - (N))) != 0); \
+ X = X >> (N); \
+ } \
+ while (0)
+
+#define __FP_FRAC_SRS_1(X, N, sz) \
+ (X = (X >> (N) | (__builtin_constant_p (N) && (N) == 1 \
+ ? X & 1 \
+ : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
+
+#define _FP_FRAC_ADD_1(R, X, Y) (R##_f = X##_f + Y##_f)
+#define _FP_FRAC_SUB_1(R, X, Y) (R##_f = X##_f - Y##_f)
+#define _FP_FRAC_DEC_1(X, Y) (X##_f -= Y##_f)
+#define _FP_FRAC_CLZ_1(z, X) __FP_CLZ ((z), X##_f)
+
+/* Predicates. */
+#define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE) X##_f < 0)
+#define _FP_FRAC_ZEROP_1(X) (X##_f == 0)
+#define _FP_FRAC_OVERP_1(fs, X) (X##_f & _FP_OVERFLOW_##fs)
+#define _FP_FRAC_CLEAR_OVERP_1(fs, X) (X##_f &= ~_FP_OVERFLOW_##fs)
+#define _FP_FRAC_HIGHBIT_DW_1(fs, X) (X##_f & _FP_HIGHBIT_DW_##fs)
+#define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f)
+#define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f)
+#define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f)
+
+#define _FP_ZEROFRAC_1 0
+#define _FP_MINFRAC_1 1
+#define _FP_MAXFRAC_1 (~(_FP_WS_TYPE) 0)
+
+/* Unpack the raw bits of a native fp value. Do not classify or
+ normalize the data. */
+
+#define _FP_UNPACK_RAW_1(fs, X, val) \
+ do \
+ { \
+ union _FP_UNION_##fs _FP_UNPACK_RAW_1_flo; \
+ _FP_UNPACK_RAW_1_flo.flt = (val); \
+ \
+ X##_f = _FP_UNPACK_RAW_1_flo.bits.frac; \
+ X##_e = _FP_UNPACK_RAW_1_flo.bits.exp; \
+ X##_s = _FP_UNPACK_RAW_1_flo.bits.sign; \
+ } \
+ while (0)
+
+#define _FP_UNPACK_RAW_1_P(fs, X, val) \
+ do \
+ { \
+ union _FP_UNION_##fs *_FP_UNPACK_RAW_1_P_flo \
+ = (union _FP_UNION_##fs *) (val); \
+ \
+ X##_f = _FP_UNPACK_RAW_1_P_flo->bits.frac; \
+ X##_e = _FP_UNPACK_RAW_1_P_flo->bits.exp; \
+ X##_s = _FP_UNPACK_RAW_1_P_flo->bits.sign; \
+ } \
+ while (0)
+
+/* Repack the raw bits of a native fp value. */
+
+#define _FP_PACK_RAW_1(fs, val, X) \
+ do \
+ { \
+ union _FP_UNION_##fs _FP_PACK_RAW_1_flo; \
+ \
+ _FP_PACK_RAW_1_flo.bits.frac = X##_f; \
+ _FP_PACK_RAW_1_flo.bits.exp = X##_e; \
+ _FP_PACK_RAW_1_flo.bits.sign = X##_s; \
+ \
+ (val) = _FP_PACK_RAW_1_flo.flt; \
+ } \
+ while (0)
+
+#define _FP_PACK_RAW_1_P(fs, val, X) \
+ do \
+ { \
+ union _FP_UNION_##fs *_FP_PACK_RAW_1_P_flo \
+ = (union _FP_UNION_##fs *) (val); \
+ \
+ _FP_PACK_RAW_1_P_flo->bits.frac = X##_f; \
+ _FP_PACK_RAW_1_P_flo->bits.exp = X##_e; \
+ _FP_PACK_RAW_1_P_flo->bits.sign = X##_s; \
+ } \
+ while (0)
+
+
+/* Multiplication algorithms: */
+
+/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
+ multiplication immediately. */
+
+#define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y) \
+ do \
+ { \
+ R##_f = X##_f * Y##_f; \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \
+ do \
+ { \
+ _FP_MUL_MEAT_DW_1_imm ((wfracbits), R, X, Y); \
+ /* Normalize since we know where the msb of the multiplicands \
+ were (bit B), we know that the msb of the of the product is \
+ at either 2B or 2B-1. */ \
+ _FP_FRAC_SRS_1 (R, (wfracbits)-1, 2*(wfracbits)); \
+ } \
+ while (0)
+
+/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
+
+#define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ doit (R##_f1, R##_f0, X##_f, Y##_f); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_wide_Z); \
+ _FP_MUL_MEAT_DW_1_wide ((wfracbits), _FP_MUL_MEAT_1_wide_Z, \
+ X, Y, doit); \
+ /* Normalize since we know where the msb of the multiplicands \
+ were (bit B), we know that the msb of the of the product is \
+ at either 2B or 2B-1. */ \
+ _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_wide_Z, (wfracbits)-1, \
+ 2*(wfracbits)); \
+ R##_f = _FP_MUL_MEAT_1_wide_Z_f0; \
+ } \
+ while (0)
+
+/* Finally, a simple widening multiply algorithm. What fun! */
+
+#define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y) \
+ do \
+ { \
+ _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_xh, _FP_MUL_MEAT_DW_1_hard_xl; \
+ _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_yh, _FP_MUL_MEAT_DW_1_hard_yl; \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_1_hard_a); \
+ \
+ /* Split the words in half. */ \
+ _FP_MUL_MEAT_DW_1_hard_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \
+ _FP_MUL_MEAT_DW_1_hard_xl \
+ = X##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
+ _FP_MUL_MEAT_DW_1_hard_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \
+ _FP_MUL_MEAT_DW_1_hard_yl \
+ = Y##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
+ \
+ /* Multiply the pieces. */ \
+ R##_f0 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yl; \
+ _FP_MUL_MEAT_DW_1_hard_a_f0 \
+ = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yl; \
+ _FP_MUL_MEAT_DW_1_hard_a_f1 \
+ = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yh; \
+ R##_f1 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yh; \
+ \
+ /* Reassemble into two full words. */ \
+ if ((_FP_MUL_MEAT_DW_1_hard_a_f0 += _FP_MUL_MEAT_DW_1_hard_a_f1) \
+ < _FP_MUL_MEAT_DW_1_hard_a_f1) \
+ R##_f1 += (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2); \
+ _FP_MUL_MEAT_DW_1_hard_a_f1 \
+ = _FP_MUL_MEAT_DW_1_hard_a_f0 >> (_FP_W_TYPE_SIZE/2); \
+ _FP_MUL_MEAT_DW_1_hard_a_f0 \
+ = _FP_MUL_MEAT_DW_1_hard_a_f0 << (_FP_W_TYPE_SIZE/2); \
+ _FP_FRAC_ADD_2 (R, R, _FP_MUL_MEAT_DW_1_hard_a); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \
+ do \
+ { \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_hard_z); \
+ _FP_MUL_MEAT_DW_1_hard ((wfracbits), \
+ _FP_MUL_MEAT_1_hard_z, X, Y); \
+ \
+ /* Normalize. */ \
+ _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_hard_z, \
+ (wfracbits) - 1, 2*(wfracbits)); \
+ R##_f = _FP_MUL_MEAT_1_hard_z_f0; \
+ } \
+ while (0)
+
+
+/* Division algorithms: */
+
+/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
+ division immediately. Give this macro either _FP_DIV_HELP_imm for
+ C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you
+ choose will depend on what the compiler does with divrem4. */
+
+#define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \
+ do \
+ { \
+ _FP_W_TYPE _FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r; \
+ X##_f <<= (X##_f < Y##_f \
+ ? R##_e--, _FP_WFRACBITS_##fs \
+ : _FP_WFRACBITS_##fs - 1); \
+ doit (_FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r, X##_f, Y##_f); \
+ R##_f = _FP_DIV_MEAT_1_imm_q | (_FP_DIV_MEAT_1_imm_r != 0); \
+ } \
+ while (0)
+
+/* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
+ that may be useful in this situation. This first is for a primitive
+ that requires normalization, the second for one that does not. Look
+ for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */
+
+#define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \
+ do \
+ { \
+ _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nh; \
+ _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nl; \
+ _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_q; \
+ _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_r; \
+ _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_y; \
+ \
+ /* Normalize Y -- i.e. make the most significant bit set. */ \
+ _FP_DIV_MEAT_1_udiv_norm_y = Y##_f << _FP_WFRACXBITS_##fs; \
+ \
+ /* Shift X op correspondingly high, that is, up one full word. */ \
+ if (X##_f < Y##_f) \
+ { \
+ R##_e--; \
+ _FP_DIV_MEAT_1_udiv_norm_nl = 0; \
+ _FP_DIV_MEAT_1_udiv_norm_nh = X##_f; \
+ } \
+ else \
+ { \
+ _FP_DIV_MEAT_1_udiv_norm_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \
+ _FP_DIV_MEAT_1_udiv_norm_nh = X##_f >> 1; \
+ } \
+ \
+ udiv_qrnnd (_FP_DIV_MEAT_1_udiv_norm_q, \
+ _FP_DIV_MEAT_1_udiv_norm_r, \
+ _FP_DIV_MEAT_1_udiv_norm_nh, \
+ _FP_DIV_MEAT_1_udiv_norm_nl, \
+ _FP_DIV_MEAT_1_udiv_norm_y); \
+ R##_f = (_FP_DIV_MEAT_1_udiv_norm_q \
+ | (_FP_DIV_MEAT_1_udiv_norm_r != 0)); \
+ } \
+ while (0)
+
+#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \
+ do \
+ { \
+ _FP_W_TYPE _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl; \
+ _FP_W_TYPE _FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r; \
+ if (X##_f < Y##_f) \
+ { \
+ R##_e--; \
+ _FP_DIV_MEAT_1_udiv_nl = X##_f << _FP_WFRACBITS_##fs; \
+ _FP_DIV_MEAT_1_udiv_nh = X##_f >> _FP_WFRACXBITS_##fs; \
+ } \
+ else \
+ { \
+ _FP_DIV_MEAT_1_udiv_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \
+ _FP_DIV_MEAT_1_udiv_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \
+ } \
+ udiv_qrnnd (_FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r, \
+ _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl, \
+ Y##_f); \
+ R##_f = _FP_DIV_MEAT_1_udiv_q | (_FP_DIV_MEAT_1_udiv_r != 0); \
+ } \
+ while (0)
+
+
+/* Square root algorithms:
+ We have just one right now, maybe Newton approximation
+ should be added for those machines where division is fast. */
+
+#define _FP_SQRT_MEAT_1(R, S, T, X, q) \
+ do \
+ { \
+ while ((q) != _FP_WORK_ROUND) \
+ { \
+ T##_f = S##_f + (q); \
+ if (T##_f <= X##_f) \
+ { \
+ S##_f = T##_f + (q); \
+ X##_f -= T##_f; \
+ R##_f += (q); \
+ } \
+ _FP_FRAC_SLL_1 (X, 1); \
+ (q) >>= 1; \
+ } \
+ if (X##_f) \
+ { \
+ if (S##_f < X##_f) \
+ R##_f |= _FP_WORK_ROUND; \
+ R##_f |= _FP_WORK_STICKY; \
+ } \
+ } \
+ while (0)
+
+/* Assembly/disassembly for converting to/from integral types.
+ No shifting or overflow handled here. */
+
+#define _FP_FRAC_ASSEMBLE_1(r, X, rsize) ((r) = X##_f)
+#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = (r))
+
+
+/* Convert FP values between word sizes. */
+
+#define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f)
+
+#endif /* !SOFT_FP_OP_1_H */
diff --git a/include/math-emu/op-2.h b/include/math-emu/op-2.h
new file mode 100644
index 0000000..a51eb6b
--- /dev/null
+++ b/include/math-emu/op-2.h
@@ -0,0 +1,705 @@
+/* Software floating-point emulation.
+ Basic two-word fraction declaration and manipulation.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_OP_2_H
+#define SOFT_FP_OP_2_H 1
+
+#define _FP_FRAC_DECL_2(X) \
+ _FP_W_TYPE X##_f0 _FP_ZERO_INIT, X##_f1 _FP_ZERO_INIT
+#define _FP_FRAC_COPY_2(D, S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
+#define _FP_FRAC_SET_2(X, I) __FP_FRAC_SET_2 (X, I)
+#define _FP_FRAC_HIGH_2(X) (X##_f1)
+#define _FP_FRAC_LOW_2(X) (X##_f0)
+#define _FP_FRAC_WORD_2(X, w) (X##_f##w)
+
+#define _FP_FRAC_SLL_2(X, N) \
+ (void) (((N) < _FP_W_TYPE_SIZE) \
+ ? ({ \
+ if (__builtin_constant_p (N) && (N) == 1) \
+ { \
+ X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE) (X##_f0)) < 0); \
+ X##_f0 += X##_f0; \
+ } \
+ else \
+ { \
+ X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
+ X##_f0 <<= (N); \
+ } \
+ 0; \
+ }) \
+ : ({ \
+ X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
+ X##_f0 = 0; \
+ }))
+
+
+#define _FP_FRAC_SRL_2(X, N) \
+ (void) (((N) < _FP_W_TYPE_SIZE) \
+ ? ({ \
+ X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
+ X##_f1 >>= (N); \
+ }) \
+ : ({ \
+ X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
+ X##_f1 = 0; \
+ }))
+
+/* Right shift with sticky-lsb. */
+#define _FP_FRAC_SRST_2(X, S, N, sz) \
+ (void) (((N) < _FP_W_TYPE_SIZE) \
+ ? ({ \
+ S = (__builtin_constant_p (N) && (N) == 1 \
+ ? X##_f0 & 1 \
+ : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \
+ X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \
+ X##_f1 >>= (N); \
+ }) \
+ : ({ \
+ S = ((((N) == _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \
+ | X##_f0) != 0); \
+ X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \
+ X##_f1 = 0; \
+ }))
+
+#define _FP_FRAC_SRS_2(X, N, sz) \
+ (void) (((N) < _FP_W_TYPE_SIZE) \
+ ? ({ \
+ X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \
+ | (__builtin_constant_p (N) && (N) == 1 \
+ ? X##_f0 & 1 \
+ : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
+ X##_f1 >>= (N); \
+ }) \
+ : ({ \
+ X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \
+ | ((((N) == _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \
+ | X##_f0) != 0)); \
+ X##_f1 = 0; \
+ }))
+
+#define _FP_FRAC_ADDI_2(X, I) \
+ __FP_FRAC_ADDI_2 (X##_f1, X##_f0, I)
+
+#define _FP_FRAC_ADD_2(R, X, Y) \
+ __FP_FRAC_ADD_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
+
+#define _FP_FRAC_SUB_2(R, X, Y) \
+ __FP_FRAC_SUB_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
+
+#define _FP_FRAC_DEC_2(X, Y) \
+ __FP_FRAC_DEC_2 (X##_f1, X##_f0, Y##_f1, Y##_f0)
+
+#define _FP_FRAC_CLZ_2(R, X) \
+ do \
+ { \
+ if (X##_f1) \
+ __FP_CLZ ((R), X##_f1); \
+ else \
+ { \
+ __FP_CLZ ((R), X##_f0); \
+ (R) += _FP_W_TYPE_SIZE; \
+ } \
+ } \
+ while (0)
+
+/* Predicates. */
+#define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE) X##_f1 < 0)
+#define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
+#define _FP_FRAC_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) & _FP_OVERFLOW_##fs)
+#define _FP_FRAC_CLEAR_OVERP_2(fs, X) (_FP_FRAC_HIGH_##fs (X) &= ~_FP_OVERFLOW_##fs)
+#define _FP_FRAC_HIGHBIT_DW_2(fs, X) \
+ (_FP_FRAC_HIGH_DW_##fs (X) & _FP_HIGHBIT_DW_##fs)
+#define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
+#define _FP_FRAC_GT_2(X, Y) \
+ (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
+#define _FP_FRAC_GE_2(X, Y) \
+ (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
+
+#define _FP_ZEROFRAC_2 0, 0
+#define _FP_MINFRAC_2 0, 1
+#define _FP_MAXFRAC_2 (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0)
+
+/* Internals. */
+
+#define __FP_FRAC_SET_2(X, I1, I0) (X##_f0 = I0, X##_f1 = I1)
+
+#define __FP_CLZ_2(R, xh, xl) \
+ do \
+ { \
+ if (xh) \
+ __FP_CLZ ((R), xh); \
+ else \
+ { \
+ __FP_CLZ ((R), xl); \
+ (R) += _FP_W_TYPE_SIZE; \
+ } \
+ } \
+ while (0)
+
+#if 0
+
+# ifndef __FP_FRAC_ADDI_2
+# define __FP_FRAC_ADDI_2(xh, xl, i) \
+ (xh += ((xl += i) < i))
+# endif
+# ifndef __FP_FRAC_ADD_2
+# define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
+ (rh = xh + yh + ((rl = xl + yl) < xl))
+# endif
+# ifndef __FP_FRAC_SUB_2
+# define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
+ (rh = xh - yh - ((rl = xl - yl) > xl))
+# endif
+# ifndef __FP_FRAC_DEC_2
+# define __FP_FRAC_DEC_2(xh, xl, yh, yl) \
+ do \
+ { \
+ UWtype __FP_FRAC_DEC_2_t = xl; \
+ xh -= yh + ((xl -= yl) > __FP_FRAC_DEC_2_t); \
+ } \
+ while (0)
+# endif
+
+#else
+
+# undef __FP_FRAC_ADDI_2
+# define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa (xh, xl, xh, xl, 0, i)
+# undef __FP_FRAC_ADD_2
+# define __FP_FRAC_ADD_2 add_ssaaaa
+# undef __FP_FRAC_SUB_2
+# define __FP_FRAC_SUB_2 sub_ddmmss
+# undef __FP_FRAC_DEC_2
+# define __FP_FRAC_DEC_2(xh, xl, yh, yl) \
+ sub_ddmmss (xh, xl, xh, xl, yh, yl)
+
+#endif
+
+/* Unpack the raw bits of a native fp value. Do not classify or
+ normalize the data. */
+
+#define _FP_UNPACK_RAW_2(fs, X, val) \
+ do \
+ { \
+ union _FP_UNION_##fs _FP_UNPACK_RAW_2_flo; \
+ _FP_UNPACK_RAW_2_flo.flt = (val); \
+ \
+ X##_f0 = _FP_UNPACK_RAW_2_flo.bits.frac0; \
+ X##_f1 = _FP_UNPACK_RAW_2_flo.bits.frac1; \
+ X##_e = _FP_UNPACK_RAW_2_flo.bits.exp; \
+ X##_s = _FP_UNPACK_RAW_2_flo.bits.sign; \
+ } \
+ while (0)
+
+#define _FP_UNPACK_RAW_2_P(fs, X, val) \
+ do \
+ { \
+ union _FP_UNION_##fs *_FP_UNPACK_RAW_2_P_flo \
+ = (union _FP_UNION_##fs *) (val); \
+ \
+ X##_f0 = _FP_UNPACK_RAW_2_P_flo->bits.frac0; \
+ X##_f1 = _FP_UNPACK_RAW_2_P_flo->bits.frac1; \
+ X##_e = _FP_UNPACK_RAW_2_P_flo->bits.exp; \
+ X##_s = _FP_UNPACK_RAW_2_P_flo->bits.sign; \
+ } \
+ while (0)
+
+
+/* Repack the raw bits of a native fp value. */
+
+#define _FP_PACK_RAW_2(fs, val, X) \
+ do \
+ { \
+ union _FP_UNION_##fs _FP_PACK_RAW_2_flo; \
+ \
+ _FP_PACK_RAW_2_flo.bits.frac0 = X##_f0; \
+ _FP_PACK_RAW_2_flo.bits.frac1 = X##_f1; \
+ _FP_PACK_RAW_2_flo.bits.exp = X##_e; \
+ _FP_PACK_RAW_2_flo.bits.sign = X##_s; \
+ \
+ (val) = _FP_PACK_RAW_2_flo.flt; \
+ } \
+ while (0)
+
+#define _FP_PACK_RAW_2_P(fs, val, X) \
+ do \
+ { \
+ union _FP_UNION_##fs *_FP_PACK_RAW_2_P_flo \
+ = (union _FP_UNION_##fs *) (val); \
+ \
+ _FP_PACK_RAW_2_P_flo->bits.frac0 = X##_f0; \
+ _FP_PACK_RAW_2_P_flo->bits.frac1 = X##_f1; \
+ _FP_PACK_RAW_2_P_flo->bits.exp = X##_e; \
+ _FP_PACK_RAW_2_P_flo->bits.sign = X##_s; \
+ } \
+ while (0)
+
+
+/* Multiplication algorithms: */
+
+/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
+
+#define _FP_MUL_MEAT_DW_2_wide(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_b); \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_c); \
+ \
+ doit (_FP_FRAC_WORD_4 (R, 1), _FP_FRAC_WORD_4 (R, 0), \
+ X##_f0, Y##_f0); \
+ doit (_FP_MUL_MEAT_DW_2_wide_b_f1, _FP_MUL_MEAT_DW_2_wide_b_f0, \
+ X##_f0, Y##_f1); \
+ doit (_FP_MUL_MEAT_DW_2_wide_c_f1, _FP_MUL_MEAT_DW_2_wide_c_f0, \
+ X##_f1, Y##_f0); \
+ doit (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ X##_f1, Y##_f1); \
+ \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_FRAC_WORD_4 (R, 1), 0, \
+ _FP_MUL_MEAT_DW_2_wide_b_f1, \
+ _FP_MUL_MEAT_DW_2_wide_b_f0, \
+ _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_FRAC_WORD_4 (R, 1)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_FRAC_WORD_4 (R, 1), 0, \
+ _FP_MUL_MEAT_DW_2_wide_c_f1, \
+ _FP_MUL_MEAT_DW_2_wide_c_f0, \
+ _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_FRAC_WORD_4 (R, 1)); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_z); \
+ \
+ _FP_MUL_MEAT_DW_2_wide ((wfracbits), _FP_MUL_MEAT_2_wide_z, \
+ X, Y, doit); \
+ \
+ /* Normalize since we know where the msb of the multiplicands \
+ were (bit B), we know that the msb of the of the product is \
+ at either 2B or 2B-1. */ \
+ _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_z, (wfracbits)-1, \
+ 2*(wfracbits)); \
+ R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 0); \
+ R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 1); \
+ } \
+ while (0)
+
+/* Given a 1W * 1W => 2W primitive, do the extended multiplication.
+ Do only 3 multiplications instead of four. This one is for machines
+ where multiplication is much more expensive than subtraction. */
+
+#define _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_b); \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_c); \
+ _FP_W_TYPE _FP_MUL_MEAT_DW_2_wide_3mul_d; \
+ int _FP_MUL_MEAT_DW_2_wide_3mul_c1; \
+ int _FP_MUL_MEAT_DW_2_wide_3mul_c2; \
+ \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 = X##_f0 + X##_f1; \
+ _FP_MUL_MEAT_DW_2_wide_3mul_c1 \
+ = _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 < X##_f0; \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 = Y##_f0 + Y##_f1; \
+ _FP_MUL_MEAT_DW_2_wide_3mul_c2 \
+ = _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 < Y##_f0; \
+ doit (_FP_MUL_MEAT_DW_2_wide_3mul_d, _FP_FRAC_WORD_4 (R, 0), \
+ X##_f0, Y##_f0); \
+ doit (_FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1), \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f0, \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \
+ doit (_FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \
+ _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, X##_f1, Y##_f1); \
+ \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 \
+ &= -_FP_MUL_MEAT_DW_2_wide_3mul_c2; \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 \
+ &= -_FP_MUL_MEAT_DW_2_wide_3mul_c1; \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_FRAC_WORD_4 (R, 1), \
+ (_FP_MUL_MEAT_DW_2_wide_3mul_c1 \
+ & _FP_MUL_MEAT_DW_2_wide_3mul_c2), 0, \
+ _FP_MUL_MEAT_DW_2_wide_3mul_d, \
+ 0, _FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1)); \
+ __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f0); \
+ __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_MUL_MEAT_DW_2_wide_3mul_b_f1); \
+ __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_FRAC_WORD_4 (R, 1), \
+ 0, _FP_MUL_MEAT_DW_2_wide_3mul_d, \
+ _FP_FRAC_WORD_4 (R, 0)); \
+ __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_FRAC_WORD_4 (R, 1), 0, \
+ _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \
+ _FP_MUL_MEAT_DW_2_wide_3mul_c_f0); \
+ __FP_FRAC_ADD_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2), \
+ _FP_MUL_MEAT_DW_2_wide_3mul_c_f1, \
+ _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, \
+ _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2)); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_3mul_z); \
+ \
+ _FP_MUL_MEAT_DW_2_wide_3mul ((wfracbits), \
+ _FP_MUL_MEAT_2_wide_3mul_z, \
+ X, Y, doit); \
+ \
+ /* Normalize since we know where the msb of the multiplicands \
+ were (bit B), we know that the msb of the of the product is \
+ at either 2B or 2B-1. */ \
+ _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_3mul_z, \
+ (wfracbits)-1, 2*(wfracbits)); \
+ R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 0); \
+ R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 1); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_DW_2_gmp(wfracbits, R, X, Y) \
+ do \
+ { \
+ _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_x[2]; \
+ _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_y[2]; \
+ _FP_MUL_MEAT_DW_2_gmp_x[0] = X##_f0; \
+ _FP_MUL_MEAT_DW_2_gmp_x[1] = X##_f1; \
+ _FP_MUL_MEAT_DW_2_gmp_y[0] = Y##_f0; \
+ _FP_MUL_MEAT_DW_2_gmp_y[1] = Y##_f1; \
+ \
+ mpn_mul_n (R##_f, _FP_MUL_MEAT_DW_2_gmp_x, \
+ _FP_MUL_MEAT_DW_2_gmp_y, 2); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \
+ do \
+ { \
+ _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_gmp_z); \
+ \
+ _FP_MUL_MEAT_DW_2_gmp ((wfracbits), _FP_MUL_MEAT_2_gmp_z, X, Y); \
+ \
+ /* Normalize since we know where the msb of the multiplicands \
+ were (bit B), we know that the msb of the of the product is \
+ at either 2B or 2B-1. */ \
+ _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_gmp_z, (wfracbits)-1, \
+ 2*(wfracbits)); \
+ R##_f0 = _FP_MUL_MEAT_2_gmp_z_f[0]; \
+ R##_f1 = _FP_MUL_MEAT_2_gmp_z_f[1]; \
+ } \
+ while (0)
+
+/* Do at most 120x120=240 bits multiplication using double floating
+ point multiplication. This is useful if floating point
+ multiplication has much bigger throughput than integer multiply.
+ It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
+ between 106 and 120 only.
+ Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
+ SETFETZ is a macro which will disable all FPU exceptions and set rounding
+ towards zero, RESETFE should optionally reset it back. */
+
+#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \
+ do \
+ { \
+ static const double _const[] = \
+ { \
+ /* 2^-24 */ 5.9604644775390625e-08, \
+ /* 2^-48 */ 3.5527136788005009e-15, \
+ /* 2^-72 */ 2.1175823681357508e-22, \
+ /* 2^-96 */ 1.2621774483536189e-29, \
+ /* 2^28 */ 2.68435456e+08, \
+ /* 2^4 */ 1.600000e+01, \
+ /* 2^-20 */ 9.5367431640625e-07, \
+ /* 2^-44 */ 5.6843418860808015e-14, \
+ /* 2^-68 */ 3.3881317890172014e-21, \
+ /* 2^-92 */ 2.0194839173657902e-28, \
+ /* 2^-116 */ 1.2037062152420224e-35 \
+ }; \
+ double _a240, _b240, _c240, _d240, _e240, _f240, \
+ _g240, _h240, _i240, _j240, _k240; \
+ union { double d; UDItype i; } _l240, _m240, _n240, _o240, \
+ _p240, _q240, _r240, _s240; \
+ UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \
+ \
+ _FP_STATIC_ASSERT ((wfracbits) >= 106 && (wfracbits) <= 120, \
+ "wfracbits out of range"); \
+ \
+ setfetz; \
+ \
+ _e240 = (double) (long) (X##_f0 & 0xffffff); \
+ _j240 = (double) (long) (Y##_f0 & 0xffffff); \
+ _d240 = (double) (long) ((X##_f0 >> 24) & 0xffffff); \
+ _i240 = (double) (long) ((Y##_f0 >> 24) & 0xffffff); \
+ _c240 = (double) (long) (((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \
+ _h240 = (double) (long) (((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \
+ _b240 = (double) (long) ((X##_f1 >> 8) & 0xffffff); \
+ _g240 = (double) (long) ((Y##_f1 >> 8) & 0xffffff); \
+ _a240 = (double) (long) (X##_f1 >> 32); \
+ _f240 = (double) (long) (Y##_f1 >> 32); \
+ _e240 *= _const[3]; \
+ _j240 *= _const[3]; \
+ _d240 *= _const[2]; \
+ _i240 *= _const[2]; \
+ _c240 *= _const[1]; \
+ _h240 *= _const[1]; \
+ _b240 *= _const[0]; \
+ _g240 *= _const[0]; \
+ _s240.d = _e240*_j240; \
+ _r240.d = _d240*_j240 + _e240*_i240; \
+ _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240; \
+ _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240; \
+ _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240; \
+ _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \
+ _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \
+ _l240.d = _a240*_g240 + _b240*_f240; \
+ _k240 = _a240*_f240; \
+ _r240.d += _s240.d; \
+ _q240.d += _r240.d; \
+ _p240.d += _q240.d; \
+ _o240.d += _p240.d; \
+ _n240.d += _o240.d; \
+ _m240.d += _n240.d; \
+ _l240.d += _m240.d; \
+ _k240 += _l240.d; \
+ _s240.d -= ((_const[10]+_s240.d)-_const[10]); \
+ _r240.d -= ((_const[9]+_r240.d)-_const[9]); \
+ _q240.d -= ((_const[8]+_q240.d)-_const[8]); \
+ _p240.d -= ((_const[7]+_p240.d)-_const[7]); \
+ _o240.d += _const[7]; \
+ _n240.d += _const[6]; \
+ _m240.d += _const[5]; \
+ _l240.d += _const[4]; \
+ if (_s240.d != 0.0) \
+ _y240 = 1; \
+ if (_r240.d != 0.0) \
+ _y240 = 1; \
+ if (_q240.d != 0.0) \
+ _y240 = 1; \
+ if (_p240.d != 0.0) \
+ _y240 = 1; \
+ _t240 = (DItype) _k240; \
+ _u240 = _l240.i; \
+ _v240 = _m240.i; \
+ _w240 = _n240.i; \
+ _x240 = _o240.i; \
+ R##_f1 = ((_t240 << (128 - (wfracbits - 1))) \
+ | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104))); \
+ R##_f0 = (((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \
+ | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \
+ | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \
+ | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \
+ | _y240); \
+ resetfe; \
+ } \
+ while (0)
+
+/* Division algorithms: */
+
+#define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \
+ do \
+ { \
+ _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f2; \
+ _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f1; \
+ _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f0; \
+ _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f1; \
+ _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f0; \
+ _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f1; \
+ _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f0; \
+ if (_FP_FRAC_GE_2 (X, Y)) \
+ { \
+ _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1 >> 1; \
+ _FP_DIV_MEAT_2_udiv_n_f1 \
+ = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
+ _FP_DIV_MEAT_2_udiv_n_f0 \
+ = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
+ } \
+ else \
+ { \
+ R##_e--; \
+ _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1; \
+ _FP_DIV_MEAT_2_udiv_n_f1 = X##_f0; \
+ _FP_DIV_MEAT_2_udiv_n_f0 = 0; \
+ } \
+ \
+ /* Normalize, i.e. make the most significant bit of the \
+ denominator set. */ \
+ _FP_FRAC_SLL_2 (Y, _FP_WFRACXBITS_##fs); \
+ \
+ udiv_qrnnd (R##_f1, _FP_DIV_MEAT_2_udiv_r_f1, \
+ _FP_DIV_MEAT_2_udiv_n_f2, _FP_DIV_MEAT_2_udiv_n_f1, \
+ Y##_f1); \
+ umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, _FP_DIV_MEAT_2_udiv_m_f0, \
+ R##_f1, Y##_f0); \
+ _FP_DIV_MEAT_2_udiv_r_f0 = _FP_DIV_MEAT_2_udiv_n_f0; \
+ if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, _FP_DIV_MEAT_2_udiv_r)) \
+ { \
+ R##_f1--; \
+ _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \
+ _FP_DIV_MEAT_2_udiv_r); \
+ if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \
+ && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \
+ _FP_DIV_MEAT_2_udiv_r)) \
+ { \
+ R##_f1--; \
+ _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \
+ _FP_DIV_MEAT_2_udiv_r); \
+ } \
+ } \
+ _FP_FRAC_DEC_2 (_FP_DIV_MEAT_2_udiv_r, _FP_DIV_MEAT_2_udiv_m); \
+ \
+ if (_FP_DIV_MEAT_2_udiv_r_f1 == Y##_f1) \
+ { \
+ /* This is a special case, not an optimization \
+ (_FP_DIV_MEAT_2_udiv_r/Y##_f1 would not fit into UWtype). \
+ As _FP_DIV_MEAT_2_udiv_r is guaranteed to be < Y, \
+ R##_f0 can be either (UWtype)-1 or (UWtype)-2. But as we \
+ know what kind of bits it is (sticky, guard, round), \
+ we don't care. We also don't care what the reminder is, \
+ because the guard bit will be set anyway. -jj */ \
+ R##_f0 = -1; \
+ } \
+ else \
+ { \
+ udiv_qrnnd (R##_f0, _FP_DIV_MEAT_2_udiv_r_f1, \
+ _FP_DIV_MEAT_2_udiv_r_f1, \
+ _FP_DIV_MEAT_2_udiv_r_f0, Y##_f1); \
+ umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, \
+ _FP_DIV_MEAT_2_udiv_m_f0, R##_f0, Y##_f0); \
+ _FP_DIV_MEAT_2_udiv_r_f0 = 0; \
+ if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \
+ _FP_DIV_MEAT_2_udiv_r)) \
+ { \
+ R##_f0--; \
+ _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \
+ _FP_DIV_MEAT_2_udiv_r); \
+ if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y) \
+ && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, \
+ _FP_DIV_MEAT_2_udiv_r)) \
+ { \
+ R##_f0--; \
+ _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y, \
+ _FP_DIV_MEAT_2_udiv_r); \
+ } \
+ } \
+ if (!_FP_FRAC_EQ_2 (_FP_DIV_MEAT_2_udiv_r, \
+ _FP_DIV_MEAT_2_udiv_m)) \
+ R##_f0 |= _FP_WORK_STICKY; \
+ } \
+ } \
+ while (0)
+
+
+/* Square root algorithms:
+ We have just one right now, maybe Newton approximation
+ should be added for those machines where division is fast. */
+
+#define _FP_SQRT_MEAT_2(R, S, T, X, q) \
+ do \
+ { \
+ while (q) \
+ { \
+ T##_f1 = S##_f1 + (q); \
+ if (T##_f1 <= X##_f1) \
+ { \
+ S##_f1 = T##_f1 + (q); \
+ X##_f1 -= T##_f1; \
+ R##_f1 += (q); \
+ } \
+ _FP_FRAC_SLL_2 (X, 1); \
+ (q) >>= 1; \
+ } \
+ (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
+ while ((q) != _FP_WORK_ROUND) \
+ { \
+ T##_f0 = S##_f0 + (q); \
+ T##_f1 = S##_f1; \
+ if (T##_f1 < X##_f1 \
+ || (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \
+ { \
+ S##_f0 = T##_f0 + (q); \
+ S##_f1 += (T##_f0 > S##_f0); \
+ _FP_FRAC_DEC_2 (X, T); \
+ R##_f0 += (q); \
+ } \
+ _FP_FRAC_SLL_2 (X, 1); \
+ (q) >>= 1; \
+ } \
+ if (X##_f0 | X##_f1) \
+ { \
+ if (S##_f1 < X##_f1 \
+ || (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \
+ R##_f0 |= _FP_WORK_ROUND; \
+ R##_f0 |= _FP_WORK_STICKY; \
+ } \
+ } \
+ while (0)
+
+
+/* Assembly/disassembly for converting to/from integral types.
+ No shifting or overflow handled here. */
+
+#define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
+ (void) (((rsize) <= _FP_W_TYPE_SIZE) \
+ ? ({ (r) = X##_f0; }) \
+ : ({ \
+ (r) = X##_f1; \
+ (r) <<= _FP_W_TYPE_SIZE; \
+ (r) += X##_f0; \
+ }))
+
+#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
+ do \
+ { \
+ X##_f0 = (r); \
+ X##_f1 = ((rsize) <= _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) >> _FP_W_TYPE_SIZE); \
+ } \
+ while (0)
+
+/* Convert FP values between word sizes. */
+
+#define _FP_FRAC_COPY_1_2(D, S) (D##_f = S##_f0)
+
+#define _FP_FRAC_COPY_2_1(D, S) ((D##_f0 = S##_f), (D##_f1 = 0))
+
+#define _FP_FRAC_COPY_2_2(D, S) _FP_FRAC_COPY_2 (D, S)
+
+#endif /* !SOFT_FP_OP_2_H */
diff --git a/include/math-emu/op-4.h b/include/math-emu/op-4.h
new file mode 100644
index 0000000..a580517
--- /dev/null
+++ b/include/math-emu/op-4.h
@@ -0,0 +1,875 @@
+/* Software floating-point emulation.
+ Basic four-word fraction declaration and manipulation.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_OP_4_H
+#define SOFT_FP_OP_4_H 1
+
+#define _FP_FRAC_DECL_4(X) _FP_W_TYPE X##_f[4]
+#define _FP_FRAC_COPY_4(D, S) \
+ (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1], \
+ D##_f[2] = S##_f[2], D##_f[3] = S##_f[3])
+#define _FP_FRAC_SET_4(X, I) __FP_FRAC_SET_4 (X, I)
+#define _FP_FRAC_HIGH_4(X) (X##_f[3])
+#define _FP_FRAC_LOW_4(X) (X##_f[0])
+#define _FP_FRAC_WORD_4(X, w) (X##_f[w])
+
+#define _FP_FRAC_SLL_4(X, N) \
+ do \
+ { \
+ _FP_I_TYPE _FP_FRAC_SLL_4_up, _FP_FRAC_SLL_4_down; \
+ _FP_I_TYPE _FP_FRAC_SLL_4_skip, _FP_FRAC_SLL_4_i; \
+ _FP_FRAC_SLL_4_skip = (N) / _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SLL_4_up = (N) % _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SLL_4_down = _FP_W_TYPE_SIZE - _FP_FRAC_SLL_4_up; \
+ if (!_FP_FRAC_SLL_4_up) \
+ for (_FP_FRAC_SLL_4_i = 3; \
+ _FP_FRAC_SLL_4_i >= _FP_FRAC_SLL_4_skip; \
+ --_FP_FRAC_SLL_4_i) \
+ X##_f[_FP_FRAC_SLL_4_i] \
+ = X##_f[_FP_FRAC_SLL_4_i-_FP_FRAC_SLL_4_skip]; \
+ else \
+ { \
+ for (_FP_FRAC_SLL_4_i = 3; \
+ _FP_FRAC_SLL_4_i > _FP_FRAC_SLL_4_skip; \
+ --_FP_FRAC_SLL_4_i) \
+ X##_f[_FP_FRAC_SLL_4_i] \
+ = ((X##_f[_FP_FRAC_SLL_4_i-_FP_FRAC_SLL_4_skip] \
+ << _FP_FRAC_SLL_4_up) \
+ | (X##_f[_FP_FRAC_SLL_4_i-_FP_FRAC_SLL_4_skip-1] \
+ >> _FP_FRAC_SLL_4_down)); \
+ X##_f[_FP_FRAC_SLL_4_i--] = X##_f[0] << _FP_FRAC_SLL_4_up; \
+ } \
+ for (; _FP_FRAC_SLL_4_i >= 0; --_FP_FRAC_SLL_4_i) \
+ X##_f[_FP_FRAC_SLL_4_i] = 0; \
+ } \
+ while (0)
+
+/* This one was broken too. */
+#define _FP_FRAC_SRL_4(X, N) \
+ do \
+ { \
+ _FP_I_TYPE _FP_FRAC_SRL_4_up, _FP_FRAC_SRL_4_down; \
+ _FP_I_TYPE _FP_FRAC_SRL_4_skip, _FP_FRAC_SRL_4_i; \
+ _FP_FRAC_SRL_4_skip = (N) / _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRL_4_down = (N) % _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRL_4_up = _FP_W_TYPE_SIZE - _FP_FRAC_SRL_4_down; \
+ if (!_FP_FRAC_SRL_4_down) \
+ for (_FP_FRAC_SRL_4_i = 0; \
+ _FP_FRAC_SRL_4_i <= 3-_FP_FRAC_SRL_4_skip; \
+ ++_FP_FRAC_SRL_4_i) \
+ X##_f[_FP_FRAC_SRL_4_i] \
+ = X##_f[_FP_FRAC_SRL_4_i+_FP_FRAC_SRL_4_skip]; \
+ else \
+ { \
+ for (_FP_FRAC_SRL_4_i = 0; \
+ _FP_FRAC_SRL_4_i < 3-_FP_FRAC_SRL_4_skip; \
+ ++_FP_FRAC_SRL_4_i) \
+ X##_f[_FP_FRAC_SRL_4_i] \
+ = ((X##_f[_FP_FRAC_SRL_4_i+_FP_FRAC_SRL_4_skip] \
+ >> _FP_FRAC_SRL_4_down) \
+ | (X##_f[_FP_FRAC_SRL_4_i+_FP_FRAC_SRL_4_skip+1] \
+ << _FP_FRAC_SRL_4_up)); \
+ X##_f[_FP_FRAC_SRL_4_i++] = X##_f[3] >> _FP_FRAC_SRL_4_down; \
+ } \
+ for (; _FP_FRAC_SRL_4_i < 4; ++_FP_FRAC_SRL_4_i) \
+ X##_f[_FP_FRAC_SRL_4_i] = 0; \
+ } \
+ while (0)
+
+
+/* Right shift with sticky-lsb.
+ What this actually means is that we do a standard right-shift,
+ but that if any of the bits that fall off the right hand side
+ were one then we always set the LSbit. */
+#define _FP_FRAC_SRST_4(X, S, N, size) \
+ do \
+ { \
+ _FP_I_TYPE _FP_FRAC_SRST_4_up, _FP_FRAC_SRST_4_down; \
+ _FP_I_TYPE _FP_FRAC_SRST_4_skip, _FP_FRAC_SRST_4_i; \
+ _FP_W_TYPE _FP_FRAC_SRST_4_s; \
+ _FP_FRAC_SRST_4_skip = (N) / _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRST_4_down = (N) % _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRST_4_up = _FP_W_TYPE_SIZE - _FP_FRAC_SRST_4_down; \
+ for (_FP_FRAC_SRST_4_s = _FP_FRAC_SRST_4_i = 0; \
+ _FP_FRAC_SRST_4_i < _FP_FRAC_SRST_4_skip; \
+ ++_FP_FRAC_SRST_4_i) \
+ _FP_FRAC_SRST_4_s |= X##_f[_FP_FRAC_SRST_4_i]; \
+ if (!_FP_FRAC_SRST_4_down) \
+ for (_FP_FRAC_SRST_4_i = 0; \
+ _FP_FRAC_SRST_4_i <= 3-_FP_FRAC_SRST_4_skip; \
+ ++_FP_FRAC_SRST_4_i) \
+ X##_f[_FP_FRAC_SRST_4_i] \
+ = X##_f[_FP_FRAC_SRST_4_i+_FP_FRAC_SRST_4_skip]; \
+ else \
+ { \
+ _FP_FRAC_SRST_4_s \
+ |= X##_f[_FP_FRAC_SRST_4_i] << _FP_FRAC_SRST_4_up; \
+ for (_FP_FRAC_SRST_4_i = 0; \
+ _FP_FRAC_SRST_4_i < 3-_FP_FRAC_SRST_4_skip; \
+ ++_FP_FRAC_SRST_4_i) \
+ X##_f[_FP_FRAC_SRST_4_i] \
+ = ((X##_f[_FP_FRAC_SRST_4_i+_FP_FRAC_SRST_4_skip] \
+ >> _FP_FRAC_SRST_4_down) \
+ | (X##_f[_FP_FRAC_SRST_4_i+_FP_FRAC_SRST_4_skip+1] \
+ << _FP_FRAC_SRST_4_up)); \
+ X##_f[_FP_FRAC_SRST_4_i++] \
+ = X##_f[3] >> _FP_FRAC_SRST_4_down; \
+ } \
+ for (; _FP_FRAC_SRST_4_i < 4; ++_FP_FRAC_SRST_4_i) \
+ X##_f[_FP_FRAC_SRST_4_i] = 0; \
+ S = (_FP_FRAC_SRST_4_s != 0); \
+ } \
+ while (0)
+
+#define _FP_FRAC_SRS_4(X, N, size) \
+ do \
+ { \
+ int _FP_FRAC_SRS_4_sticky; \
+ _FP_FRAC_SRST_4 (X, _FP_FRAC_SRS_4_sticky, (N), (size)); \
+ X##_f[0] |= _FP_FRAC_SRS_4_sticky; \
+ } \
+ while (0)
+
+#define _FP_FRAC_ADD_4(R, X, Y) \
+ __FP_FRAC_ADD_4 (R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
+ X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
+ Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
+
+#define _FP_FRAC_SUB_4(R, X, Y) \
+ __FP_FRAC_SUB_4 (R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
+ X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
+ Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
+
+#define _FP_FRAC_DEC_4(X, Y) \
+ __FP_FRAC_DEC_4 (X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
+ Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
+
+#define _FP_FRAC_ADDI_4(X, I) \
+ __FP_FRAC_ADDI_4 (X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
+
+#define _FP_ZEROFRAC_4 0, 0, 0, 0
+#define _FP_MINFRAC_4 0, 0, 0, 1
+#define _FP_MAXFRAC_4 (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0)
+
+#define _FP_FRAC_ZEROP_4(X) ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
+#define _FP_FRAC_NEGP_4(X) ((_FP_WS_TYPE) X##_f[3] < 0)
+#define _FP_FRAC_OVERP_4(fs, X) (_FP_FRAC_HIGH_##fs (X) & _FP_OVERFLOW_##fs)
+#define _FP_FRAC_HIGHBIT_DW_4(fs, X) \
+ (_FP_FRAC_HIGH_DW_##fs (X) & _FP_HIGHBIT_DW_##fs)
+#define _FP_FRAC_CLEAR_OVERP_4(fs, X) (_FP_FRAC_HIGH_##fs (X) &= ~_FP_OVERFLOW_##fs)
+
+#define _FP_FRAC_EQ_4(X, Y) \
+ (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1] \
+ && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
+
+#define _FP_FRAC_GT_4(X, Y) \
+ (X##_f[3] > Y##_f[3] \
+ || (X##_f[3] == Y##_f[3] \
+ && (X##_f[2] > Y##_f[2] \
+ || (X##_f[2] == Y##_f[2] \
+ && (X##_f[1] > Y##_f[1] \
+ || (X##_f[1] == Y##_f[1] \
+ && X##_f[0] > Y##_f[0]))))))
+
+#define _FP_FRAC_GE_4(X, Y) \
+ (X##_f[3] > Y##_f[3] \
+ || (X##_f[3] == Y##_f[3] \
+ && (X##_f[2] > Y##_f[2] \
+ || (X##_f[2] == Y##_f[2] \
+ && (X##_f[1] > Y##_f[1] \
+ || (X##_f[1] == Y##_f[1] \
+ && X##_f[0] >= Y##_f[0]))))))
+
+
+#define _FP_FRAC_CLZ_4(R, X) \
+ do \
+ { \
+ if (X##_f[3]) \
+ __FP_CLZ ((R), X##_f[3]); \
+ else if (X##_f[2]) \
+ { \
+ __FP_CLZ ((R), X##_f[2]); \
+ (R) += _FP_W_TYPE_SIZE; \
+ } \
+ else if (X##_f[1]) \
+ { \
+ __FP_CLZ ((R), X##_f[1]); \
+ (R) += _FP_W_TYPE_SIZE*2; \
+ } \
+ else \
+ { \
+ __FP_CLZ ((R), X##_f[0]); \
+ (R) += _FP_W_TYPE_SIZE*3; \
+ } \
+ } \
+ while (0)
+
+
+#define _FP_UNPACK_RAW_4(fs, X, val) \
+ do \
+ { \
+ union _FP_UNION_##fs _FP_UNPACK_RAW_4_flo; \
+ _FP_UNPACK_RAW_4_flo.flt = (val); \
+ X##_f[0] = _FP_UNPACK_RAW_4_flo.bits.frac0; \
+ X##_f[1] = _FP_UNPACK_RAW_4_flo.bits.frac1; \
+ X##_f[2] = _FP_UNPACK_RAW_4_flo.bits.frac2; \
+ X##_f[3] = _FP_UNPACK_RAW_4_flo.bits.frac3; \
+ X##_e = _FP_UNPACK_RAW_4_flo.bits.exp; \
+ X##_s = _FP_UNPACK_RAW_4_flo.bits.sign; \
+ } \
+ while (0)
+
+#define _FP_UNPACK_RAW_4_P(fs, X, val) \
+ do \
+ { \
+ union _FP_UNION_##fs *_FP_UNPACK_RAW_4_P_flo \
+ = (union _FP_UNION_##fs *) (val); \
+ \
+ X##_f[0] = _FP_UNPACK_RAW_4_P_flo->bits.frac0; \
+ X##_f[1] = _FP_UNPACK_RAW_4_P_flo->bits.frac1; \
+ X##_f[2] = _FP_UNPACK_RAW_4_P_flo->bits.frac2; \
+ X##_f[3] = _FP_UNPACK_RAW_4_P_flo->bits.frac3; \
+ X##_e = _FP_UNPACK_RAW_4_P_flo->bits.exp; \
+ X##_s = _FP_UNPACK_RAW_4_P_flo->bits.sign; \
+ } \
+ while (0)
+
+#define _FP_PACK_RAW_4(fs, val, X) \
+ do \
+ { \
+ union _FP_UNION_##fs _FP_PACK_RAW_4_flo; \
+ _FP_PACK_RAW_4_flo.bits.frac0 = X##_f[0]; \
+ _FP_PACK_RAW_4_flo.bits.frac1 = X##_f[1]; \
+ _FP_PACK_RAW_4_flo.bits.frac2 = X##_f[2]; \
+ _FP_PACK_RAW_4_flo.bits.frac3 = X##_f[3]; \
+ _FP_PACK_RAW_4_flo.bits.exp = X##_e; \
+ _FP_PACK_RAW_4_flo.bits.sign = X##_s; \
+ (val) = _FP_PACK_RAW_4_flo.flt; \
+ } \
+ while (0)
+
+#define _FP_PACK_RAW_4_P(fs, val, X) \
+ do \
+ { \
+ union _FP_UNION_##fs *_FP_PACK_RAW_4_P_flo \
+ = (union _FP_UNION_##fs *) (val); \
+ \
+ _FP_PACK_RAW_4_P_flo->bits.frac0 = X##_f[0]; \
+ _FP_PACK_RAW_4_P_flo->bits.frac1 = X##_f[1]; \
+ _FP_PACK_RAW_4_P_flo->bits.frac2 = X##_f[2]; \
+ _FP_PACK_RAW_4_P_flo->bits.frac3 = X##_f[3]; \
+ _FP_PACK_RAW_4_P_flo->bits.exp = X##_e; \
+ _FP_PACK_RAW_4_P_flo->bits.sign = X##_s; \
+ } \
+ while (0)
+
+/* Multiplication algorithms: */
+
+/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
+
+#define _FP_MUL_MEAT_DW_4_wide(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_4_wide_b); \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_4_wide_c); \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_4_wide_d); \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_4_wide_e); \
+ _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_4_wide_f); \
+ \
+ doit (_FP_FRAC_WORD_8 (R, 1), _FP_FRAC_WORD_8 (R, 0), \
+ X##_f[0], Y##_f[0]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_b_f1, _FP_MUL_MEAT_DW_4_wide_b_f0, \
+ X##_f[0], Y##_f[1]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_c_f1, _FP_MUL_MEAT_DW_4_wide_c_f0, \
+ X##_f[1], Y##_f[0]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_d_f1, _FP_MUL_MEAT_DW_4_wide_d_f0, \
+ X##_f[1], Y##_f[1]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_e_f1, _FP_MUL_MEAT_DW_4_wide_e_f0, \
+ X##_f[0], Y##_f[2]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_f_f1, _FP_MUL_MEAT_DW_4_wide_f_f0, \
+ X##_f[2], Y##_f[0]); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2), \
+ _FP_FRAC_WORD_8 (R, 1), 0, \
+ _FP_MUL_MEAT_DW_4_wide_b_f1, \
+ _FP_MUL_MEAT_DW_4_wide_b_f0, \
+ 0, 0, _FP_FRAC_WORD_8 (R, 1)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2), \
+ _FP_FRAC_WORD_8 (R, 1), 0, \
+ _FP_MUL_MEAT_DW_4_wide_c_f1, \
+ _FP_MUL_MEAT_DW_4_wide_c_f0, \
+ _FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2), \
+ _FP_FRAC_WORD_8 (R, 1)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \
+ _FP_FRAC_WORD_8 (R, 2), 0, \
+ _FP_MUL_MEAT_DW_4_wide_d_f1, \
+ _FP_MUL_MEAT_DW_4_wide_d_f0, \
+ 0, _FP_FRAC_WORD_8 (R, 3), _FP_FRAC_WORD_8 (R, 2)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \
+ _FP_FRAC_WORD_8 (R, 2), 0, \
+ _FP_MUL_MEAT_DW_4_wide_e_f1, \
+ _FP_MUL_MEAT_DW_4_wide_e_f0, \
+ _FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \
+ _FP_FRAC_WORD_8 (R, 2)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \
+ _FP_FRAC_WORD_8 (R, 2), 0, \
+ _FP_MUL_MEAT_DW_4_wide_f_f1, \
+ _FP_MUL_MEAT_DW_4_wide_f_f0, \
+ _FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3), \
+ _FP_FRAC_WORD_8 (R, 2)); \
+ doit (_FP_MUL_MEAT_DW_4_wide_b_f1, \
+ _FP_MUL_MEAT_DW_4_wide_b_f0, X##_f[0], Y##_f[3]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_c_f1, \
+ _FP_MUL_MEAT_DW_4_wide_c_f0, X##_f[3], Y##_f[0]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_d_f1, _FP_MUL_MEAT_DW_4_wide_d_f0, \
+ X##_f[1], Y##_f[2]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_e_f1, _FP_MUL_MEAT_DW_4_wide_e_f0, \
+ X##_f[2], Y##_f[1]); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \
+ _FP_FRAC_WORD_8 (R, 3), 0, \
+ _FP_MUL_MEAT_DW_4_wide_b_f1, \
+ _FP_MUL_MEAT_DW_4_wide_b_f0, \
+ 0, _FP_FRAC_WORD_8 (R, 4), _FP_FRAC_WORD_8 (R, 3)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \
+ _FP_FRAC_WORD_8 (R, 3), 0, \
+ _FP_MUL_MEAT_DW_4_wide_c_f1, \
+ _FP_MUL_MEAT_DW_4_wide_c_f0, \
+ _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \
+ _FP_FRAC_WORD_8 (R, 3)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \
+ _FP_FRAC_WORD_8 (R, 3), 0, \
+ _FP_MUL_MEAT_DW_4_wide_d_f1, \
+ _FP_MUL_MEAT_DW_4_wide_d_f0, \
+ _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \
+ _FP_FRAC_WORD_8 (R, 3)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \
+ _FP_FRAC_WORD_8 (R, 3), 0, \
+ _FP_MUL_MEAT_DW_4_wide_e_f1, \
+ _FP_MUL_MEAT_DW_4_wide_e_f0, \
+ _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4), \
+ _FP_FRAC_WORD_8 (R, 3)); \
+ doit (_FP_MUL_MEAT_DW_4_wide_b_f1, _FP_MUL_MEAT_DW_4_wide_b_f0, \
+ X##_f[2], Y##_f[2]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_c_f1, _FP_MUL_MEAT_DW_4_wide_c_f0, \
+ X##_f[1], Y##_f[3]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_d_f1, _FP_MUL_MEAT_DW_4_wide_d_f0, \
+ X##_f[3], Y##_f[1]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_e_f1, _FP_MUL_MEAT_DW_4_wide_e_f0, \
+ X##_f[2], Y##_f[3]); \
+ doit (_FP_MUL_MEAT_DW_4_wide_f_f1, _FP_MUL_MEAT_DW_4_wide_f_f0, \
+ X##_f[3], Y##_f[2]); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \
+ _FP_FRAC_WORD_8 (R, 4), 0, \
+ _FP_MUL_MEAT_DW_4_wide_b_f1, \
+ _FP_MUL_MEAT_DW_4_wide_b_f0, \
+ 0, _FP_FRAC_WORD_8 (R, 5), _FP_FRAC_WORD_8 (R, 4)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \
+ _FP_FRAC_WORD_8 (R, 4), 0, \
+ _FP_MUL_MEAT_DW_4_wide_c_f1, \
+ _FP_MUL_MEAT_DW_4_wide_c_f0, \
+ _FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \
+ _FP_FRAC_WORD_8 (R, 4)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \
+ _FP_FRAC_WORD_8 (R, 4), 0, \
+ _FP_MUL_MEAT_DW_4_wide_d_f1, \
+ _FP_MUL_MEAT_DW_4_wide_d_f0, \
+ _FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5), \
+ _FP_FRAC_WORD_8 (R, 4)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \
+ _FP_FRAC_WORD_8 (R, 5), 0, \
+ _FP_MUL_MEAT_DW_4_wide_e_f1, \
+ _FP_MUL_MEAT_DW_4_wide_e_f0, \
+ 0, _FP_FRAC_WORD_8 (R, 6), _FP_FRAC_WORD_8 (R, 5)); \
+ __FP_FRAC_ADD_3 (_FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \
+ _FP_FRAC_WORD_8 (R, 5), 0, \
+ _FP_MUL_MEAT_DW_4_wide_f_f1, \
+ _FP_MUL_MEAT_DW_4_wide_f_f0, \
+ _FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \
+ _FP_FRAC_WORD_8 (R, 5)); \
+ doit (_FP_MUL_MEAT_DW_4_wide_b_f1, _FP_MUL_MEAT_DW_4_wide_b_f0, \
+ X##_f[3], Y##_f[3]); \
+ __FP_FRAC_ADD_2 (_FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6), \
+ _FP_MUL_MEAT_DW_4_wide_b_f1, \
+ _FP_MUL_MEAT_DW_4_wide_b_f0, \
+ _FP_FRAC_WORD_8 (R, 7), _FP_FRAC_WORD_8 (R, 6)); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit) \
+ do \
+ { \
+ _FP_FRAC_DECL_8 (_FP_MUL_MEAT_4_wide_z); \
+ \
+ _FP_MUL_MEAT_DW_4_wide ((wfracbits), _FP_MUL_MEAT_4_wide_z, \
+ X, Y, doit); \
+ \
+ /* Normalize since we know where the msb of the multiplicands \
+ were (bit B), we know that the msb of the of the product is \
+ at either 2B or 2B-1. */ \
+ _FP_FRAC_SRS_8 (_FP_MUL_MEAT_4_wide_z, (wfracbits)-1, \
+ 2*(wfracbits)); \
+ __FP_FRAC_SET_4 (R, _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_wide_z, 3), \
+ _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_wide_z, 2), \
+ _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_wide_z, 1), \
+ _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_wide_z, 0)); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_DW_4_gmp(wfracbits, R, X, Y) \
+ do \
+ { \
+ mpn_mul_n (R##_f, _x_f, _y_f, 4); \
+ } \
+ while (0)
+
+#define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y) \
+ do \
+ { \
+ _FP_FRAC_DECL_8 (_FP_MUL_MEAT_4_gmp_z); \
+ \
+ _FP_MUL_MEAT_DW_4_gmp ((wfracbits), _FP_MUL_MEAT_4_gmp_z, X, Y); \
+ \
+ /* Normalize since we know where the msb of the multiplicands \
+ were (bit B), we know that the msb of the of the product is \
+ at either 2B or 2B-1. */ \
+ _FP_FRAC_SRS_8 (_FP_MUL_MEAT_4_gmp_z, (wfracbits)-1, \
+ 2*(wfracbits)); \
+ __FP_FRAC_SET_4 (R, _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_gmp_z, 3), \
+ _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_gmp_z, 2), \
+ _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_gmp_z, 1), \
+ _FP_FRAC_WORD_8 (_FP_MUL_MEAT_4_gmp_z, 0)); \
+ } \
+ while (0)
+
+/* Helper utility for _FP_DIV_MEAT_4_udiv:
+ * pppp = m * nnn. */
+#define umul_ppppmnnn(p3, p2, p1, p0, m, n2, n1, n0) \
+ do \
+ { \
+ UWtype umul_ppppmnnn_t; \
+ umul_ppmm (p1, p0, m, n0); \
+ umul_ppmm (p2, umul_ppppmnnn_t, m, n1); \
+ __FP_FRAC_ADDI_2 (p2, p1, umul_ppppmnnn_t); \
+ umul_ppmm (p3, umul_ppppmnnn_t, m, n2); \
+ __FP_FRAC_ADDI_2 (p3, p2, umul_ppppmnnn_t); \
+ } \
+ while (0)
+
+/* Division algorithms: */
+
+#define _FP_DIV_MEAT_4_udiv(fs, R, X, Y) \
+ do \
+ { \
+ int _FP_DIV_MEAT_4_udiv_i; \
+ _FP_FRAC_DECL_4 (_FP_DIV_MEAT_4_udiv_n); \
+ _FP_FRAC_DECL_4 (_FP_DIV_MEAT_4_udiv_m); \
+ _FP_FRAC_SET_4 (_FP_DIV_MEAT_4_udiv_n, _FP_ZEROFRAC_4); \
+ if (_FP_FRAC_GE_4 (X, Y)) \
+ { \
+ _FP_DIV_MEAT_4_udiv_n_f[3] \
+ = X##_f[0] << (_FP_W_TYPE_SIZE - 1); \
+ _FP_FRAC_SRL_4 (X, 1); \
+ } \
+ else \
+ R##_e--; \
+ \
+ /* Normalize, i.e. make the most significant bit of the \
+ denominator set. */ \
+ _FP_FRAC_SLL_4 (Y, _FP_WFRACXBITS_##fs); \
+ \
+ for (_FP_DIV_MEAT_4_udiv_i = 3; ; _FP_DIV_MEAT_4_udiv_i--) \
+ { \
+ if (X##_f[3] == Y##_f[3]) \
+ { \
+ /* This is a special case, not an optimization \
+ (X##_f[3]/Y##_f[3] would not fit into UWtype). \
+ As X## is guaranteed to be < Y, \
+ R##_f[_FP_DIV_MEAT_4_udiv_i] can be either \
+ (UWtype)-1 or (UWtype)-2. */ \
+ R##_f[_FP_DIV_MEAT_4_udiv_i] = -1; \
+ if (!_FP_DIV_MEAT_4_udiv_i) \
+ break; \
+ __FP_FRAC_SUB_4 (X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
+ Y##_f[2], Y##_f[1], Y##_f[0], 0, \
+ X##_f[2], X##_f[1], X##_f[0], \
+ _FP_DIV_MEAT_4_udiv_n_f[_FP_DIV_MEAT_4_udiv_i]); \
+ _FP_FRAC_SUB_4 (X, Y, X); \
+ if (X##_f[3] > Y##_f[3]) \
+ { \
+ R##_f[_FP_DIV_MEAT_4_udiv_i] = -2; \
+ _FP_FRAC_ADD_4 (X, Y, X); \
+ } \
+ } \
+ else \
+ { \
+ udiv_qrnnd (R##_f[_FP_DIV_MEAT_4_udiv_i], \
+ X##_f[3], X##_f[3], X##_f[2], Y##_f[3]); \
+ umul_ppppmnnn (_FP_DIV_MEAT_4_udiv_m_f[3], \
+ _FP_DIV_MEAT_4_udiv_m_f[2], \
+ _FP_DIV_MEAT_4_udiv_m_f[1], \
+ _FP_DIV_MEAT_4_udiv_m_f[0], \
+ R##_f[_FP_DIV_MEAT_4_udiv_i], \
+ Y##_f[2], Y##_f[1], Y##_f[0]); \
+ X##_f[2] = X##_f[1]; \
+ X##_f[1] = X##_f[0]; \
+ X##_f[0] \
+ = _FP_DIV_MEAT_4_udiv_n_f[_FP_DIV_MEAT_4_udiv_i]; \
+ if (_FP_FRAC_GT_4 (_FP_DIV_MEAT_4_udiv_m, X)) \
+ { \
+ R##_f[_FP_DIV_MEAT_4_udiv_i]--; \
+ _FP_FRAC_ADD_4 (X, Y, X); \
+ if (_FP_FRAC_GE_4 (X, Y) \
+ && _FP_FRAC_GT_4 (_FP_DIV_MEAT_4_udiv_m, X)) \
+ { \
+ R##_f[_FP_DIV_MEAT_4_udiv_i]--; \
+ _FP_FRAC_ADD_4 (X, Y, X); \
+ } \
+ } \
+ _FP_FRAC_DEC_4 (X, _FP_DIV_MEAT_4_udiv_m); \
+ if (!_FP_DIV_MEAT_4_udiv_i) \
+ { \
+ if (!_FP_FRAC_EQ_4 (X, _FP_DIV_MEAT_4_udiv_m)) \
+ R##_f[0] |= _FP_WORK_STICKY; \
+ break; \
+ } \
+ } \
+ } \
+ } \
+ while (0)
+
+
+/* Square root algorithms:
+ We have just one right now, maybe Newton approximation
+ should be added for those machines where division is fast. */
+
+#define _FP_SQRT_MEAT_4(R, S, T, X, q) \
+ do \
+ { \
+ while (q) \
+ { \
+ T##_f[3] = S##_f[3] + (q); \
+ if (T##_f[3] <= X##_f[3]) \
+ { \
+ S##_f[3] = T##_f[3] + (q); \
+ X##_f[3] -= T##_f[3]; \
+ R##_f[3] += (q); \
+ } \
+ _FP_FRAC_SLL_4 (X, 1); \
+ (q) >>= 1; \
+ } \
+ (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
+ while (q) \
+ { \
+ T##_f[2] = S##_f[2] + (q); \
+ T##_f[3] = S##_f[3]; \
+ if (T##_f[3] < X##_f[3] \
+ || (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2])) \
+ { \
+ S##_f[2] = T##_f[2] + (q); \
+ S##_f[3] += (T##_f[2] > S##_f[2]); \
+ __FP_FRAC_DEC_2 (X##_f[3], X##_f[2], \
+ T##_f[3], T##_f[2]); \
+ R##_f[2] += (q); \
+ } \
+ _FP_FRAC_SLL_4 (X, 1); \
+ (q) >>= 1; \
+ } \
+ (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
+ while (q) \
+ { \
+ T##_f[1] = S##_f[1] + (q); \
+ T##_f[2] = S##_f[2]; \
+ T##_f[3] = S##_f[3]; \
+ if (T##_f[3] < X##_f[3] \
+ || (T##_f[3] == X##_f[3] \
+ && (T##_f[2] < X##_f[2] \
+ || (T##_f[2] == X##_f[2] \
+ && T##_f[1] <= X##_f[1])))) \
+ { \
+ S##_f[1] = T##_f[1] + (q); \
+ S##_f[2] += (T##_f[1] > S##_f[1]); \
+ S##_f[3] += (T##_f[2] > S##_f[2]); \
+ __FP_FRAC_DEC_3 (X##_f[3], X##_f[2], X##_f[1], \
+ T##_f[3], T##_f[2], T##_f[1]); \
+ R##_f[1] += (q); \
+ } \
+ _FP_FRAC_SLL_4 (X, 1); \
+ (q) >>= 1; \
+ } \
+ (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
+ while ((q) != _FP_WORK_ROUND) \
+ { \
+ T##_f[0] = S##_f[0] + (q); \
+ T##_f[1] = S##_f[1]; \
+ T##_f[2] = S##_f[2]; \
+ T##_f[3] = S##_f[3]; \
+ if (_FP_FRAC_GE_4 (X, T)) \
+ { \
+ S##_f[0] = T##_f[0] + (q); \
+ S##_f[1] += (T##_f[0] > S##_f[0]); \
+ S##_f[2] += (T##_f[1] > S##_f[1]); \
+ S##_f[3] += (T##_f[2] > S##_f[2]); \
+ _FP_FRAC_DEC_4 (X, T); \
+ R##_f[0] += (q); \
+ } \
+ _FP_FRAC_SLL_4 (X, 1); \
+ (q) >>= 1; \
+ } \
+ if (!_FP_FRAC_ZEROP_4 (X)) \
+ { \
+ if (_FP_FRAC_GT_4 (X, S)) \
+ R##_f[0] |= _FP_WORK_ROUND; \
+ R##_f[0] |= _FP_WORK_STICKY; \
+ } \
+ } \
+ while (0)
+
+
+/* Internals. */
+
+#define __FP_FRAC_SET_4(X, I3, I2, I1, I0) \
+ (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
+
+#ifndef __FP_FRAC_ADD_3
+# define __FP_FRAC_ADD_3(r2, r1, r0, x2, x1, x0, y2, y1, y0) \
+ do \
+ { \
+ _FP_W_TYPE __FP_FRAC_ADD_3_c1, __FP_FRAC_ADD_3_c2; \
+ r0 = x0 + y0; \
+ __FP_FRAC_ADD_3_c1 = r0 < x0; \
+ r1 = x1 + y1; \
+ __FP_FRAC_ADD_3_c2 = r1 < x1; \
+ r1 += __FP_FRAC_ADD_3_c1; \
+ __FP_FRAC_ADD_3_c2 |= r1 < __FP_FRAC_ADD_3_c1; \
+ r2 = x2 + y2 + __FP_FRAC_ADD_3_c2; \
+ } \
+ while (0)
+#endif
+
+#ifndef __FP_FRAC_ADD_4
+# define __FP_FRAC_ADD_4(r3, r2, r1, r0, x3, x2, x1, x0, y3, y2, y1, y0) \
+ do \
+ { \
+ _FP_W_TYPE __FP_FRAC_ADD_4_c1, __FP_FRAC_ADD_4_c2; \
+ _FP_W_TYPE __FP_FRAC_ADD_4_c3; \
+ r0 = x0 + y0; \
+ __FP_FRAC_ADD_4_c1 = r0 < x0; \
+ r1 = x1 + y1; \
+ __FP_FRAC_ADD_4_c2 = r1 < x1; \
+ r1 += __FP_FRAC_ADD_4_c1; \
+ __FP_FRAC_ADD_4_c2 |= r1 < __FP_FRAC_ADD_4_c1; \
+ r2 = x2 + y2; \
+ __FP_FRAC_ADD_4_c3 = r2 < x2; \
+ r2 += __FP_FRAC_ADD_4_c2; \
+ __FP_FRAC_ADD_4_c3 |= r2 < __FP_FRAC_ADD_4_c2; \
+ r3 = x3 + y3 + __FP_FRAC_ADD_4_c3; \
+ } \
+ while (0)
+#endif
+
+#ifndef __FP_FRAC_SUB_3
+# define __FP_FRAC_SUB_3(r2, r1, r0, x2, x1, x0, y2, y1, y0) \
+ do \
+ { \
+ _FP_W_TYPE __FP_FRAC_SUB_3_c1, __FP_FRAC_SUB_3_c2; \
+ r0 = x0 - y0; \
+ __FP_FRAC_SUB_3_c1 = r0 > x0; \
+ r1 = x1 - y1; \
+ __FP_FRAC_SUB_3_c2 = r1 > x1; \
+ r1 -= __FP_FRAC_SUB_3_c1; \
+ __FP_FRAC_SUB_3_c2 |= __FP_FRAC_SUB_3_c1 && (y1 == x1); \
+ r2 = x2 - y2 - __FP_FRAC_SUB_3_c2; \
+ } \
+ while (0)
+#endif
+
+#ifndef __FP_FRAC_SUB_4
+# define __FP_FRAC_SUB_4(r3, r2, r1, r0, x3, x2, x1, x0, y3, y2, y1, y0) \
+ do \
+ { \
+ _FP_W_TYPE __FP_FRAC_SUB_4_c1, __FP_FRAC_SUB_4_c2; \
+ _FP_W_TYPE __FP_FRAC_SUB_4_c3; \
+ r0 = x0 - y0; \
+ __FP_FRAC_SUB_4_c1 = r0 > x0; \
+ r1 = x1 - y1; \
+ __FP_FRAC_SUB_4_c2 = r1 > x1; \
+ r1 -= __FP_FRAC_SUB_4_c1; \
+ __FP_FRAC_SUB_4_c2 |= __FP_FRAC_SUB_4_c1 && (y1 == x1); \
+ r2 = x2 - y2; \
+ __FP_FRAC_SUB_4_c3 = r2 > x2; \
+ r2 -= __FP_FRAC_SUB_4_c2; \
+ __FP_FRAC_SUB_4_c3 |= __FP_FRAC_SUB_4_c2 && (y2 == x2); \
+ r3 = x3 - y3 - __FP_FRAC_SUB_4_c3; \
+ } \
+ while (0)
+#endif
+
+#ifndef __FP_FRAC_DEC_3
+# define __FP_FRAC_DEC_3(x2, x1, x0, y2, y1, y0) \
+ do \
+ { \
+ UWtype __FP_FRAC_DEC_3_t0, __FP_FRAC_DEC_3_t1; \
+ UWtype __FP_FRAC_DEC_3_t2; \
+ __FP_FRAC_DEC_3_t0 = x0; \
+ __FP_FRAC_DEC_3_t1 = x1; \
+ __FP_FRAC_DEC_3_t2 = x2; \
+ __FP_FRAC_SUB_3 (x2, x1, x0, __FP_FRAC_DEC_3_t2, \
+ __FP_FRAC_DEC_3_t1, __FP_FRAC_DEC_3_t0, \
+ y2, y1, y0); \
+ } \
+ while (0)
+#endif
+
+#ifndef __FP_FRAC_DEC_4
+# define __FP_FRAC_DEC_4(x3, x2, x1, x0, y3, y2, y1, y0) \
+ do \
+ { \
+ UWtype __FP_FRAC_DEC_4_t0, __FP_FRAC_DEC_4_t1; \
+ UWtype __FP_FRAC_DEC_4_t2, __FP_FRAC_DEC_4_t3; \
+ __FP_FRAC_DEC_4_t0 = x0; \
+ __FP_FRAC_DEC_4_t1 = x1; \
+ __FP_FRAC_DEC_4_t2 = x2; \
+ __FP_FRAC_DEC_4_t3 = x3; \
+ __FP_FRAC_SUB_4 (x3, x2, x1, x0, __FP_FRAC_DEC_4_t3, \
+ __FP_FRAC_DEC_4_t2, __FP_FRAC_DEC_4_t1, \
+ __FP_FRAC_DEC_4_t0, y3, y2, y1, y0); \
+ } \
+ while (0)
+#endif
+
+#ifndef __FP_FRAC_ADDI_4
+# define __FP_FRAC_ADDI_4(x3, x2, x1, x0, i) \
+ do \
+ { \
+ UWtype __FP_FRAC_ADDI_4_t; \
+ __FP_FRAC_ADDI_4_t = ((x0 += i) < i); \
+ x1 += __FP_FRAC_ADDI_4_t; \
+ __FP_FRAC_ADDI_4_t = (x1 < __FP_FRAC_ADDI_4_t); \
+ x2 += __FP_FRAC_ADDI_4_t; \
+ __FP_FRAC_ADDI_4_t = (x2 < __FP_FRAC_ADDI_4_t); \
+ x3 += __FP_FRAC_ADDI_4_t; \
+ } \
+ while (0)
+#endif
+
+/* Convert FP values between word sizes. This appears to be more
+ complicated than I'd have expected it to be, so these might be
+ wrong... These macros are in any case somewhat bogus because they
+ use information about what various FRAC_n variables look like
+ internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
+ the ones in op-2.h and op-1.h. */
+#define _FP_FRAC_COPY_1_4(D, S) (D##_f = S##_f[0])
+
+#define _FP_FRAC_COPY_2_4(D, S) \
+ do \
+ { \
+ D##_f0 = S##_f[0]; \
+ D##_f1 = S##_f[1]; \
+ } \
+ while (0)
+
+/* Assembly/disassembly for converting to/from integral types.
+ No shifting or overflow handled here. */
+/* Put the FP value X into r, which is an integer of size rsize. */
+#define _FP_FRAC_ASSEMBLE_4(r, X, rsize) \
+ do \
+ { \
+ if ((rsize) <= _FP_W_TYPE_SIZE) \
+ (r) = X##_f[0]; \
+ else if ((rsize) <= 2*_FP_W_TYPE_SIZE) \
+ { \
+ (r) = X##_f[1]; \
+ (r) = ((rsize) <= _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) << _FP_W_TYPE_SIZE); \
+ (r) += X##_f[0]; \
+ } \
+ else \
+ { \
+ /* I'm feeling lazy so we deal with int == 3words \
+ (implausible) and int == 4words as a single case. */ \
+ (r) = X##_f[3]; \
+ (r) = ((rsize) <= _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) << _FP_W_TYPE_SIZE); \
+ (r) += X##_f[2]; \
+ (r) = ((rsize) <= _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) << _FP_W_TYPE_SIZE); \
+ (r) += X##_f[1]; \
+ (r) = ((rsize) <= _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) << _FP_W_TYPE_SIZE); \
+ (r) += X##_f[0]; \
+ } \
+ } \
+ while (0)
+
+/* "No disassemble Number Five!" */
+/* Move an integer of size rsize into X's fractional part. We rely on
+ the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
+ having to mask the values we store into it. */
+#define _FP_FRAC_DISASSEMBLE_4(X, r, rsize) \
+ do \
+ { \
+ X##_f[0] = (r); \
+ X##_f[1] = ((rsize) <= _FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) >> _FP_W_TYPE_SIZE); \
+ X##_f[2] = ((rsize) <= 2*_FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) >> 2*_FP_W_TYPE_SIZE); \
+ X##_f[3] = ((rsize) <= 3*_FP_W_TYPE_SIZE \
+ ? 0 \
+ : (r) >> 3*_FP_W_TYPE_SIZE); \
+ } \
+ while (0)
+
+#define _FP_FRAC_COPY_4_1(D, S) \
+ do \
+ { \
+ D##_f[0] = S##_f; \
+ D##_f[1] = D##_f[2] = D##_f[3] = 0; \
+ } \
+ while (0)
+
+#define _FP_FRAC_COPY_4_2(D, S) \
+ do \
+ { \
+ D##_f[0] = S##_f0; \
+ D##_f[1] = S##_f1; \
+ D##_f[2] = D##_f[3] = 0; \
+ } \
+ while (0)
+
+#define _FP_FRAC_COPY_4_4(D, S) _FP_FRAC_COPY_4 (D, S)
+
+#endif /* !SOFT_FP_OP_4_H */
diff --git a/include/math-emu/op-8.h b/include/math-emu/op-8.h
new file mode 100644
index 0000000..5267ae3
--- /dev/null
+++ b/include/math-emu/op-8.h
@@ -0,0 +1,150 @@
+/* Software floating-point emulation.
+ Basic eight-word fraction declaration and manipulation.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_OP_8_H
+#define SOFT_FP_OP_8_H 1
+
+/* We need just a few things from here for op-4, if we ever need some
+ other macros, they can be added. */
+#define _FP_FRAC_DECL_8(X) _FP_W_TYPE X##_f[8]
+#define _FP_FRAC_HIGH_8(X) (X##_f[7])
+#define _FP_FRAC_LOW_8(X) (X##_f[0])
+#define _FP_FRAC_WORD_8(X, w) (X##_f[w])
+
+#define _FP_FRAC_SLL_8(X, N) \
+ do \
+ { \
+ _FP_I_TYPE _FP_FRAC_SLL_8_up, _FP_FRAC_SLL_8_down; \
+ _FP_I_TYPE _FP_FRAC_SLL_8_skip, _FP_FRAC_SLL_8_i; \
+ _FP_FRAC_SLL_8_skip = (N) / _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SLL_8_up = (N) % _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SLL_8_down = _FP_W_TYPE_SIZE - _FP_FRAC_SLL_8_up; \
+ if (!_FP_FRAC_SLL_8_up) \
+ for (_FP_FRAC_SLL_8_i = 7; \
+ _FP_FRAC_SLL_8_i >= _FP_FRAC_SLL_8_skip; \
+ --_FP_FRAC_SLL_8_i) \
+ X##_f[_FP_FRAC_SLL_8_i] \
+ = X##_f[_FP_FRAC_SLL_8_i-_FP_FRAC_SLL_8_skip]; \
+ else \
+ { \
+ for (_FP_FRAC_SLL_8_i = 7; \
+ _FP_FRAC_SLL_8_i > _FP_FRAC_SLL_8_skip; \
+ --_FP_FRAC_SLL_8_i) \
+ X##_f[_FP_FRAC_SLL_8_i] \
+ = ((X##_f[_FP_FRAC_SLL_8_i-_FP_FRAC_SLL_8_skip] \
+ << _FP_FRAC_SLL_8_up) \
+ | (X##_f[_FP_FRAC_SLL_8_i-_FP_FRAC_SLL_8_skip-1] \
+ >> _FP_FRAC_SLL_8_down)); \
+ X##_f[_FP_FRAC_SLL_8_i--] = X##_f[0] << _FP_FRAC_SLL_8_up; \
+ } \
+ for (; _FP_FRAC_SLL_8_i >= 0; --_FP_FRAC_SLL_8_i) \
+ X##_f[_FP_FRAC_SLL_8_i] = 0; \
+ } \
+ while (0)
+
+#define _FP_FRAC_SRL_8(X, N) \
+ do \
+ { \
+ _FP_I_TYPE _FP_FRAC_SRL_8_up, _FP_FRAC_SRL_8_down; \
+ _FP_I_TYPE _FP_FRAC_SRL_8_skip, _FP_FRAC_SRL_8_i; \
+ _FP_FRAC_SRL_8_skip = (N) / _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRL_8_down = (N) % _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRL_8_up = _FP_W_TYPE_SIZE - _FP_FRAC_SRL_8_down; \
+ if (!_FP_FRAC_SRL_8_down) \
+ for (_FP_FRAC_SRL_8_i = 0; \
+ _FP_FRAC_SRL_8_i <= 7-_FP_FRAC_SRL_8_skip; \
+ ++_FP_FRAC_SRL_8_i) \
+ X##_f[_FP_FRAC_SRL_8_i] \
+ = X##_f[_FP_FRAC_SRL_8_i+_FP_FRAC_SRL_8_skip]; \
+ else \
+ { \
+ for (_FP_FRAC_SRL_8_i = 0; \
+ _FP_FRAC_SRL_8_i < 7-_FP_FRAC_SRL_8_skip; \
+ ++_FP_FRAC_SRL_8_i) \
+ X##_f[_FP_FRAC_SRL_8_i] \
+ = ((X##_f[_FP_FRAC_SRL_8_i+_FP_FRAC_SRL_8_skip] \
+ >> _FP_FRAC_SRL_8_down) \
+ | (X##_f[_FP_FRAC_SRL_8_i+_FP_FRAC_SRL_8_skip+1] \
+ << _FP_FRAC_SRL_8_up)); \
+ X##_f[_FP_FRAC_SRL_8_i++] = X##_f[7] >> _FP_FRAC_SRL_8_down; \
+ } \
+ for (; _FP_FRAC_SRL_8_i < 8; ++_FP_FRAC_SRL_8_i) \
+ X##_f[_FP_FRAC_SRL_8_i] = 0; \
+ } \
+ while (0)
+
+
+/* Right shift with sticky-lsb.
+ What this actually means is that we do a standard right-shift,
+ but that if any of the bits that fall off the right hand side
+ were one then we always set the LSbit. */
+#define _FP_FRAC_SRS_8(X, N, size) \
+ do \
+ { \
+ _FP_I_TYPE _FP_FRAC_SRS_8_up, _FP_FRAC_SRS_8_down; \
+ _FP_I_TYPE _FP_FRAC_SRS_8_skip, _FP_FRAC_SRS_8_i; \
+ _FP_W_TYPE _FP_FRAC_SRS_8_s; \
+ _FP_FRAC_SRS_8_skip = (N) / _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRS_8_down = (N) % _FP_W_TYPE_SIZE; \
+ _FP_FRAC_SRS_8_up = _FP_W_TYPE_SIZE - _FP_FRAC_SRS_8_down; \
+ for (_FP_FRAC_SRS_8_s = _FP_FRAC_SRS_8_i = 0; \
+ _FP_FRAC_SRS_8_i < _FP_FRAC_SRS_8_skip; \
+ ++_FP_FRAC_SRS_8_i) \
+ _FP_FRAC_SRS_8_s |= X##_f[_FP_FRAC_SRS_8_i]; \
+ if (!_FP_FRAC_SRS_8_down) \
+ for (_FP_FRAC_SRS_8_i = 0; \
+ _FP_FRAC_SRS_8_i <= 7-_FP_FRAC_SRS_8_skip; \
+ ++_FP_FRAC_SRS_8_i) \
+ X##_f[_FP_FRAC_SRS_8_i] \
+ = X##_f[_FP_FRAC_SRS_8_i+_FP_FRAC_SRS_8_skip]; \
+ else \
+ { \
+ _FP_FRAC_SRS_8_s \
+ |= X##_f[_FP_FRAC_SRS_8_i] << _FP_FRAC_SRS_8_up; \
+ for (_FP_FRAC_SRS_8_i = 0; \
+ _FP_FRAC_SRS_8_i < 7-_FP_FRAC_SRS_8_skip; \
+ ++_FP_FRAC_SRS_8_i) \
+ X##_f[_FP_FRAC_SRS_8_i] \
+ = ((X##_f[_FP_FRAC_SRS_8_i+_FP_FRAC_SRS_8_skip] \
+ >> _FP_FRAC_SRS_8_down) \
+ | (X##_f[_FP_FRAC_SRS_8_i+_FP_FRAC_SRS_8_skip+1] \
+ << _FP_FRAC_SRS_8_up)); \
+ X##_f[_FP_FRAC_SRS_8_i++] = X##_f[7] >> _FP_FRAC_SRS_8_down; \
+ } \
+ for (; _FP_FRAC_SRS_8_i < 8; ++_FP_FRAC_SRS_8_i) \
+ X##_f[_FP_FRAC_SRS_8_i] = 0; \
+ /* Don't fix the LSB until the very end when we're sure f[0] is \
+ stable. */ \
+ X##_f[0] |= (_FP_FRAC_SRS_8_s != 0); \
+ } \
+ while (0)
+
+#endif /* !SOFT_FP_OP_8_H */
diff --git a/include/math-emu/op-common.h b/include/math-emu/op-common.h
new file mode 100644
index 0000000..080ef0e
--- /dev/null
+++ b/include/math-emu/op-common.h
@@ -0,0 +1,2129 @@
+/* Software floating-point emulation. Common operations.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_OP_COMMON_H
+#define SOFT_FP_OP_COMMON_H 1
+
+#define _FP_DECL(wc, X) \
+ _FP_I_TYPE X##_c __attribute__ ((unused)) _FP_ZERO_INIT; \
+ _FP_I_TYPE X##_s __attribute__ ((unused)) _FP_ZERO_INIT; \
+ _FP_I_TYPE X##_e __attribute__ ((unused)) _FP_ZERO_INIT; \
+ _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 if (FP_DENORM_ZERO) \
+ { \
+ X##_c = FP_CLS_ZERO; \
+ _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
+ FP_SET_EXCEPTION (FP_EX_DENORM); \
+ } \
+ else \
+ { \
+ /* A denormalized number. */ \
+ _FP_I_TYPE _FP_UNPACK_CANONICAL_shift; \
+ _FP_FRAC_CLZ_##wc (_FP_UNPACK_CANONICAL_shift, \
+ X); \
+ _FP_UNPACK_CANONICAL_shift -= _FP_FRACXBITS_##fs; \
+ _FP_FRAC_SLL_##wc (X, (_FP_UNPACK_CANONICAL_shift \
+ + _FP_WORKBITS)); \
+ X##_e -= (_FP_EXPBIAS_##fs - 1 \
+ + _FP_UNPACK_CANONICAL_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 \
+ | FP_EX_INVALID_SNAN); \
+ } \
+ 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)
+
+/* Check whether a raw or semi-raw input value should be flushed to
+ zero, and flush it to zero if so. */
+#define _FP_CHECK_FLUSH_ZERO(fs, wc, X) \
+ do \
+ { \
+ if (FP_DENORM_ZERO \
+ && X##_e == 0 \
+ && !_FP_FRAC_ZEROP_##wc (X)) \
+ { \
+ _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
+ FP_SET_EXCEPTION (FP_EX_DENORM); \
+ } \
+ } \
+ while (0)
+
+/* 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 | FP_EX_INVALID_SNAN); \
+ } \
+ 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 _FP_ISSIGNAN_ret = 0; \
+ if (X##_e == _FP_EXPMAX_##fs) \
+ { \
+ if (!_FP_FRAC_ZEROP_##wc (X) \
+ && _FP_FRAC_SNANP (fs, X)) \
+ _FP_ISSIGNAN_ret = 1; \
+ } \
+ _FP_ISSIGNAN_ret; \
+ })
+
+
+
+
+
+/* Addition on semi-raw values. */
+#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
+ do \
+ { \
+ _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
+ _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
+ if (X##_s == Y##_s) \
+ { \
+ /* Addition. */ \
+ __label__ add1, add2, add3, add_done; \
+ R##_s = X##_s; \
+ int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
+ if (_FP_ADD_INTERNAL_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); \
+ _FP_ADD_INTERNAL_ediff--; \
+ if (_FP_ADD_INTERNAL_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 \
+ _FP_ADD_INTERNAL_EDIFF steps; remember to account \
+ later for the implicit MSB of X. */ \
+ if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
+ _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_ediff < 0) \
+ { \
+ _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_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); \
+ _FP_ADD_INTERNAL_ediff--; \
+ if (_FP_ADD_INTERNAL_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 \
+ _FP_ADD_INTERNAL_EDIFF steps; remember to account \
+ later for the implicit MSB of Y. */ \
+ if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
+ _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_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 \
+ { \
+ /* _FP_ADD_INTERNAL_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. */ \
+ __label__ sub1, sub2, sub3, norm, sub_done; \
+ int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
+ if (_FP_ADD_INTERNAL_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); \
+ _FP_ADD_INTERNAL_ediff--; \
+ if (_FP_ADD_INTERNAL_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 \
+ _FP_ADD_INTERNAL_EDIFF steps; remember to account \
+ later for the implicit MSB of X. */ \
+ if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
+ _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_ediff < 0) \
+ { \
+ _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_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); \
+ _FP_ADD_INTERNAL_ediff--; \
+ if (_FP_ADD_INTERNAL_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 \
+ _FP_ADD_INTERNAL_EDIFF steps; remember to account \
+ later for the implicit MSB of Y. */ \
+ if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
+ _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_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 \
+ | FP_EX_INVALID_ISI); \
+ } \
+ 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 _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_diff, R); \
+ _FP_ADD_INTERNAL_diff -= _FP_WFRACXBITS_##fs; \
+ _FP_FRAC_SLL_##wc (R, _FP_ADD_INTERNAL_diff); \
+ if (R##_e <= _FP_ADD_INTERNAL_diff) \
+ { \
+ /* R is denormalized. */ \
+ _FP_ADD_INTERNAL_diff \
+ = _FP_ADD_INTERNAL_diff - R##_e + 1; \
+ _FP_FRAC_SRS_##wc (R, _FP_ADD_INTERNAL_diff, \
+ _FP_WFRACBITS_##fs); \
+ R##_e = 0; \
+ } \
+ else \
+ { \
+ R##_e -= _FP_ADD_INTERNAL_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 | FP_EX_INVALID_IMZ); \
+ break; \
+ \
+ default: \
+ _FP_UNREACHABLE; \
+ } \
+ } \
+ while (0)
+
+
+/* Fused multiply-add. The input values should be cooked. */
+
+#define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \
+ do \
+ { \
+ __label__ done_fma; \
+ FP_DECL_##fs (_FP_FMA_T); \
+ _FP_FMA_T##_s = X##_s ^ Y##_s; \
+ _FP_FMA_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 = _FP_FMA_T##_s; \
+ R##_e = _FP_FMA_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 (_FP_FMA_TD); \
+ _FP_FRAC_DECL_##dwc (_FP_FMA_ZD); \
+ _FP_FRAC_DECL_##dwc (_FP_FMA_RD); \
+ _FP_MUL_MEAT_DW_##fs (_FP_FMA_TD, X, Y); \
+ R##_e = _FP_FMA_T##_e; \
+ int _FP_FMA_tsh \
+ = _FP_FRAC_HIGHBIT_DW_##dwc (fs, _FP_FMA_TD) == 0; \
+ _FP_FMA_T##_e -= _FP_FMA_tsh; \
+ int _FP_FMA_ediff = _FP_FMA_T##_e - Z##_e; \
+ if (_FP_FMA_ediff >= 0) \
+ { \
+ int _FP_FMA_shift \
+ = _FP_WFRACBITS_##fs - _FP_FMA_tsh - _FP_FMA_ediff; \
+ if (_FP_FMA_shift <= -_FP_WFRACBITS_##fs) \
+ _FP_FRAC_SET_##dwc (_FP_FMA_ZD, _FP_MINFRAC_##dwc); \
+ else \
+ { \
+ _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
+ if (_FP_FMA_shift < 0) \
+ _FP_FRAC_SRS_##dwc (_FP_FMA_ZD, -_FP_FMA_shift, \
+ _FP_WFRACBITS_DW_##fs); \
+ else if (_FP_FMA_shift > 0) \
+ _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_FMA_shift); \
+ } \
+ R##_s = _FP_FMA_T##_s; \
+ if (_FP_FMA_T##_s == Z##_s) \
+ _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
+ _FP_FMA_ZD); \
+ else \
+ { \
+ _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
+ _FP_FMA_ZD); \
+ if (_FP_FRAC_NEGP_##dwc (_FP_FMA_RD)) \
+ { \
+ R##_s = Z##_s; \
+ _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
+ _FP_FMA_TD); \
+ } \
+ } \
+ } \
+ else \
+ { \
+ R##_e = Z##_e; \
+ R##_s = Z##_s; \
+ _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
+ _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_WFRACBITS_##fs); \
+ int _FP_FMA_shift = -_FP_FMA_ediff - _FP_FMA_tsh; \
+ if (_FP_FMA_shift >= _FP_WFRACBITS_DW_##fs) \
+ _FP_FRAC_SET_##dwc (_FP_FMA_TD, _FP_MINFRAC_##dwc); \
+ else if (_FP_FMA_shift > 0) \
+ _FP_FRAC_SRS_##dwc (_FP_FMA_TD, _FP_FMA_shift, \
+ _FP_WFRACBITS_DW_##fs); \
+ if (Z##_s == _FP_FMA_T##_s) \
+ _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
+ _FP_FMA_TD); \
+ else \
+ _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
+ _FP_FMA_TD); \
+ } \
+ if (_FP_FRAC_ZEROP_##dwc (_FP_FMA_RD)) \
+ { \
+ if (_FP_FMA_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 _FP_FMA_rlz; \
+ _FP_FRAC_CLZ_##dwc (_FP_FMA_rlz, _FP_FMA_RD); \
+ _FP_FMA_rlz -= _FP_WFRACXBITS_DW_##fs; \
+ R##_e -= _FP_FMA_rlz; \
+ int _FP_FMA_shift = _FP_WFRACBITS_##fs - _FP_FMA_rlz; \
+ if (_FP_FMA_shift > 0) \
+ _FP_FRAC_SRS_##dwc (_FP_FMA_RD, _FP_FMA_shift, \
+ _FP_WFRACBITS_DW_##fs); \
+ else if (_FP_FMA_shift < 0) \
+ _FP_FRAC_SLL_##dwc (_FP_FMA_RD, -_FP_FMA_shift); \
+ _FP_FRAC_COPY_##wc##_##dwc (R, _FP_FMA_RD); \
+ R##_c = FP_CLS_NORMAL; \
+ } \
+ break; \
+ } \
+ goto done_fma; \
+ \
+ case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
+ _FP_CHOOSENAN (fs, wc, _FP_FMA_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): \
+ _FP_FMA_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 (_FP_FMA_T, X); \
+ _FP_FMA_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): \
+ _FP_FMA_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 (_FP_FMA_T, Y); \
+ _FP_FMA_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): \
+ _FP_FMA_T##_s = _FP_NANSIGN_##fs; \
+ _FP_FMA_T##_c = FP_CLS_NAN; \
+ _FP_FRAC_SET_##wc (_FP_FMA_T, _FP_NANFRAC_##fs); \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ_FMA); \
+ break; \
+ \
+ default: \
+ _FP_UNREACHABLE; \
+ } \
+ \
+ /* T = X * Y is zero, infinity or NaN. */ \
+ switch (_FP_CLS_COMBINE (_FP_FMA_T##_c, Z##_c)) \
+ { \
+ case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
+ _FP_CHOOSENAN (fs, wc, R, _FP_FMA_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 = _FP_FMA_T##_s; \
+ _FP_FRAC_COPY_##wc (R, _FP_FMA_T); \
+ R##_c = _FP_FMA_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; \
+ R##_e = Z##_e; \
+ break; \
+ \
+ case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
+ if (_FP_FMA_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 | FP_EX_INVALID_ISI); \
+ } \
+ break; \
+ \
+ case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
+ if (_FP_FMA_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: \
+ _FP_UNREACHABLE; \
+ } \
+ 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 \
+ | (X##_c == FP_CLS_INF \
+ ? FP_EX_INVALID_IDI \
+ : FP_EX_INVALID_ZDZ)); \
+ break; \
+ \
+ default: \
+ _FP_UNREACHABLE; \
+ } \
+ } \
+ while (0)
+
+
+/* Helper for comparisons. EX is 0 not to raise exceptions, 1 to
+ raise exceptions for signaling NaN operands, 2 to raise exceptions
+ for all NaN operands. Conditionals are organized to allow the
+ compiler to optimize away code based on the value of EX. */
+
+#define _FP_CMP_CHECK_NAN(fs, wc, X, Y, ex) \
+ do \
+ { \
+ /* The arguments are unordered, which may or may not result in \
+ an exception. */ \
+ if (ex) \
+ { \
+ /* At least some cases of unordered arguments result in \
+ exceptions; check whether this is one. */ \
+ if (FP_EX_INVALID_SNAN || FP_EX_INVALID_VC) \
+ { \
+ /* Check separately for each case of "invalid" \
+ exceptions. */ \
+ if ((ex) == 2) \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_VC); \
+ if (_FP_ISSIGNAN (fs, wc, X) \
+ || _FP_ISSIGNAN (fs, wc, Y)) \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
+ } \
+ /* Otherwise, we only need to check whether to raise an \
+ exception, not which case or cases it is. */ \
+ else if ((ex) == 2 \
+ || _FP_ISSIGNAN (fs, wc, X) \
+ || _FP_ISSIGNAN (fs, wc, Y)) \
+ FP_SET_EXCEPTION (FP_EX_INVALID); \
+ } \
+ } \
+ while (0)
+
+/* Helper for comparisons. If denormal operands would raise an
+ exception, check for them, and flush to zero as appropriate
+ (otherwise, we need only check and flush to zero if it might affect
+ the result, which is done later with _FP_CMP_CHECK_FLUSH_ZERO). */
+#define _FP_CMP_CHECK_DENORM(fs, wc, X, Y) \
+ do \
+ { \
+ if (FP_EX_DENORM != 0) \
+ { \
+ /* We must ensure the correct exceptions are raised for \
+ denormal operands, even though this may not affect the \
+ result of the comparison. */ \
+ if (FP_DENORM_ZERO) \
+ { \
+ _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
+ _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
+ } \
+ else \
+ { \
+ if ((X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X)) \
+ || (Y##_e == 0 && !_FP_FRAC_ZEROP_##wc (Y))) \
+ FP_SET_EXCEPTION (FP_EX_DENORM); \
+ } \
+ } \
+ } \
+ while (0)
+
+/* Helper for comparisons. Check for flushing denormals for zero if
+ we didn't need to check earlier for any denormal operands. */
+#define _FP_CMP_CHECK_FLUSH_ZERO(fs, wc, X, Y) \
+ do \
+ { \
+ if (FP_EX_DENORM == 0) \
+ { \
+ _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
+ _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
+ } \
+ } \
+ while (0)
+
+/* Main differential comparison routine. The inputs should be raw not
+ cooked. The return is -1, 0, 1 for normal values, UN
+ otherwise. */
+
+#define _FP_CMP(fs, wc, ret, X, Y, un, ex) \
+ do \
+ { \
+ _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
+ /* 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); \
+ _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
+ } \
+ else \
+ { \
+ int _FP_CMP_is_zero_x; \
+ int _FP_CMP_is_zero_y; \
+ \
+ _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
+ \
+ _FP_CMP_is_zero_x \
+ = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \
+ _FP_CMP_is_zero_y \
+ = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \
+ \
+ if (_FP_CMP_is_zero_x && _FP_CMP_is_zero_y) \
+ (ret) = 0; \
+ else if (_FP_CMP_is_zero_x) \
+ (ret) = Y##_s ? 1 : -1; \
+ else if (_FP_CMP_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, ex) \
+ do \
+ { \
+ _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
+ /* 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; \
+ _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
+ } \
+ else \
+ { \
+ _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
+ \
+ (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, ex) \
+ do \
+ { \
+ _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
+ (ret) = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
+ || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \
+ if (ret) \
+ _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
+ } \
+ while (0)
+
+/* Main square root routine. The input value should be cooked. */
+
+#define _FP_SQRT(fs, wc, R, X) \
+ do \
+ { \
+ _FP_FRAC_DECL_##wc (_FP_SQRT_T); \
+ _FP_FRAC_DECL_##wc (_FP_SQRT_S); \
+ _FP_W_TYPE _FP_SQRT_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 | FP_EX_INVALID_SQRT); \
+ } \
+ 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 | FP_EX_INVALID_SQRT); \
+ 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 (_FP_SQRT_S, _FP_ZEROFRAC_##wc); \
+ _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
+ _FP_SQRT_q = _FP_OVERFLOW_##fs >> 1; \
+ _FP_SQRT_MEAT_##wc (R, _FP_SQRT_S, _FP_SQRT_T, X, \
+ _FP_SQRT_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.
+ 2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
+ NV is set plus the result is reduced modulo 2^rsize.
+ -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)) \
+ { \
+ if (!FP_DENORM_ZERO) \
+ FP_SET_EXCEPTION (FP_EX_INEXACT); \
+ FP_SET_EXCEPTION (FP_EX_DENORM); \
+ } \
+ } \
+ else \
+ FP_SET_EXCEPTION (FP_EX_INEXACT); \
+ } \
+ else if ((rsigned) == 2 \
+ && (X##_e \
+ >= ((_FP_EXPMAX_##fs \
+ < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
+ ? _FP_EXPMAX_##fs \
+ : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
+ { \
+ /* Overflow resulting in 0. */ \
+ (r) = 0; \
+ FP_SET_EXCEPTION (FP_EX_INVALID \
+ | FP_EX_INVALID_CVI \
+ | ((FP_EX_INVALID_SNAN \
+ && _FP_ISSIGNAN (fs, wc, X)) \
+ ? FP_EX_INVALID_SNAN \
+ : 0)); \
+ } \
+ else if ((rsigned) != 2 \
+ && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
+ ? _FP_EXPMAX_##fs \
+ : (_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 (_FP_EXPBIAS_##fs + (rsize) - 1 < _FP_EXPMAX_##fs \
+ && (rsigned) \
+ && X##_s \
+ && X##_e == _FP_EXPBIAS_##fs + (rsize) - 1) \
+ { \
+ /* Possibly converting to most negative integer; check the \
+ mantissa. */ \
+ int _FP_TO_INT_inexact = 0; \
+ (void) ((_FP_FRACBITS_##fs > (rsize)) \
+ ? ({ \
+ _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
+ _FP_FRACBITS_##fs - (rsize), \
+ _FP_FRACBITS_##fs); \
+ 0; \
+ }) \
+ : 0); \
+ if (!_FP_FRAC_ZEROP_##wc (X)) \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
+ else if (_FP_TO_INT_inexact) \
+ FP_SET_EXCEPTION (FP_EX_INEXACT); \
+ } \
+ else \
+ FP_SET_EXCEPTION (FP_EX_INVALID \
+ | FP_EX_INVALID_CVI \
+ | ((FP_EX_INVALID_SNAN \
+ && _FP_ISSIGNAN (fs, wc, X)) \
+ ? FP_EX_INVALID_SNAN \
+ : 0)); \
+ } \
+ else \
+ { \
+ int _FP_TO_INT_inexact = 0; \
+ _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 \
+ { \
+ _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
+ (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
+ - X##_e), \
+ _FP_FRACBITS_##fs); \
+ _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
+ } \
+ if ((rsigned) && X##_s) \
+ (r) = -(r); \
+ if ((rsigned) == 2 && X##_e >= _FP_EXPBIAS_##fs + (rsize) - 1) \
+ { \
+ /* Overflow or converting to the most negative integer. */ \
+ if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
+ || !X##_s \
+ || (r) != (((typeof (r)) 1) << ((rsize) - 1))) \
+ { \
+ _FP_TO_INT_inexact = 0; \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
+ } \
+ } \
+ if (_FP_TO_INT_inexact) \
+ FP_SET_EXCEPTION (FP_EX_INEXACT); \
+ } \
+ } \
+ while (0)
+
+/* Convert from floating point to integer, rounding according to the
+ current rounding direction. Input is raw. RSIGNED is as for
+ _FP_TO_INT. */
+#define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned) \
+ do \
+ { \
+ __label__ _FP_TO_INT_ROUND_done; \
+ if (X##_e < _FP_EXPBIAS_##fs) \
+ { \
+ int _FP_TO_INT_ROUND_rounds_away = 0; \
+ if (X##_e == 0) \
+ { \
+ if (_FP_FRAC_ZEROP_##wc (X)) \
+ { \
+ (r) = 0; \
+ goto _FP_TO_INT_ROUND_done; \
+ } \
+ else \
+ { \
+ FP_SET_EXCEPTION (FP_EX_DENORM); \
+ if (FP_DENORM_ZERO) \
+ { \
+ (r) = 0; \
+ goto _FP_TO_INT_ROUND_done; \
+ } \
+ } \
+ } \
+ /* The result is 0, 1 or -1 depending on the rounding mode; \
+ -1 may cause overflow in the unsigned case. */ \
+ switch (FP_ROUNDMODE) \
+ { \
+ case FP_RND_NEAREST: \
+ _FP_TO_INT_ROUND_rounds_away \
+ = (X##_e == _FP_EXPBIAS_##fs - 1 \
+ && !_FP_FRAC_ZEROP_##wc (X)); \
+ break; \
+ case FP_RND_ZERO: \
+ /* _FP_TO_INT_ROUND_rounds_away is already 0. */ \
+ break; \
+ case FP_RND_PINF: \
+ _FP_TO_INT_ROUND_rounds_away = !X##_s; \
+ break; \
+ case FP_RND_MINF: \
+ _FP_TO_INT_ROUND_rounds_away = X##_s; \
+ break; \
+ } \
+ if ((rsigned) == 0 && _FP_TO_INT_ROUND_rounds_away && X##_s) \
+ { \
+ /* Result of -1 for an unsigned conversion. */ \
+ (r) = 0; \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
+ } \
+ else if ((rsize) == 1 && (rsigned) > 0 \
+ && _FP_TO_INT_ROUND_rounds_away && !X##_s) \
+ { \
+ /* Converting to a 1-bit signed bit-field, which cannot \
+ represent +1. */ \
+ (r) = ((rsigned) == 2 ? -1 : 0); \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
+ } \
+ else \
+ { \
+ (r) = (_FP_TO_INT_ROUND_rounds_away \
+ ? (X##_s ? -1 : 1) \
+ : 0); \
+ FP_SET_EXCEPTION (FP_EX_INEXACT); \
+ } \
+ } \
+ else if ((rsigned) == 2 \
+ && (X##_e \
+ >= ((_FP_EXPMAX_##fs \
+ < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
+ ? _FP_EXPMAX_##fs \
+ : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
+ { \
+ /* Overflow resulting in 0. */ \
+ (r) = 0; \
+ FP_SET_EXCEPTION (FP_EX_INVALID \
+ | FP_EX_INVALID_CVI \
+ | ((FP_EX_INVALID_SNAN \
+ && _FP_ISSIGNAN (fs, wc, X)) \
+ ? FP_EX_INVALID_SNAN \
+ : 0)); \
+ } \
+ else if ((rsigned) != 2 \
+ && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
+ ? _FP_EXPMAX_##fs \
+ : (_FP_EXPBIAS_##fs + (rsize) \
+ - ((rsigned) > 0 && !X##_s))) \
+ || ((rsigned) == 0 && X##_s))) \
+ { \
+ /* Definite overflow (does not require rounding to tell). */ \
+ if ((rsigned) != 0) \
+ { \
+ (r) = 1; \
+ (r) <<= (rsize) - 1; \
+ (r) -= 1 - X##_s; \
+ } \
+ else \
+ { \
+ (r) = 0; \
+ if (!X##_s) \
+ (r) = ~(r); \
+ } \
+ \
+ FP_SET_EXCEPTION (FP_EX_INVALID \
+ | FP_EX_INVALID_CVI \
+ | ((FP_EX_INVALID_SNAN \
+ && _FP_ISSIGNAN (fs, wc, X)) \
+ ? FP_EX_INVALID_SNAN \
+ : 0)); \
+ } \
+ else \
+ { \
+ /* The value is finite, with magnitude at least 1. If \
+ the conversion is unsigned, the value is positive. \
+ If RSIGNED is not 2, the value does not definitely \
+ overflow by virtue of its exponent, but may still turn \
+ out to overflow after rounding; if RSIGNED is 2, the \
+ exponent may be such that the value definitely overflows, \
+ but at least one mantissa bit will not be shifted out. */ \
+ int _FP_TO_INT_ROUND_inexact = 0; \
+ _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
+ if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
+ { \
+ /* The value is an integer, no rounding needed. */ \
+ _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
+ (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
+ } \
+ else \
+ { \
+ /* May need to shift in order to round (unless there \
+ are exactly _FP_WORKBITS fractional bits already). */ \
+ int _FP_TO_INT_ROUND_rshift \
+ = (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs \
+ - 1 - _FP_WORKBITS - X##_e); \
+ if (_FP_TO_INT_ROUND_rshift > 0) \
+ _FP_FRAC_SRS_##wc (X, _FP_TO_INT_ROUND_rshift, \
+ _FP_WFRACBITS_##fs); \
+ else if (_FP_TO_INT_ROUND_rshift < 0) \
+ _FP_FRAC_SLL_##wc (X, -_FP_TO_INT_ROUND_rshift); \
+ /* Round like _FP_ROUND, but setting \
+ _FP_TO_INT_ROUND_inexact instead of directly setting \
+ the "inexact" exception, since it may turn out we \
+ should set "invalid" instead. */ \
+ if (_FP_FRAC_LOW_##wc (X) & 7) \
+ { \
+ _FP_TO_INT_ROUND_inexact = 1; \
+ switch (FP_ROUNDMODE) \
+ { \
+ case FP_RND_NEAREST: \
+ _FP_ROUND_NEAREST (wc, X); \
+ break; \
+ case FP_RND_ZERO: \
+ _FP_ROUND_ZERO (wc, X); \
+ break; \
+ case FP_RND_PINF: \
+ _FP_ROUND_PINF (wc, X); \
+ break; \
+ case FP_RND_MINF: \
+ _FP_ROUND_MINF (wc, X); \
+ break; \
+ } \
+ } \
+ _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
+ _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
+ } \
+ if ((rsigned) != 0 && X##_s) \
+ (r) = -(r); \
+ /* An exponent of RSIZE - 1 always needs testing for \
+ overflow (either directly overflowing, or overflowing \
+ when rounding up results in 2^RSIZE). An exponent of \
+ RSIZE - 2 can overflow for positive values when rounding \
+ up to 2^(RSIZE-1), but cannot overflow for negative \
+ values. Smaller exponents cannot overflow. */ \
+ if (X##_e >= (_FP_EXPBIAS_##fs + (rsize) - 1 \
+ - ((rsigned) > 0 && !X##_s))) \
+ { \
+ if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
+ || (X##_e == _FP_EXPBIAS_##fs + (rsize) - 1 \
+ && (X##_s \
+ ? (r) != (((typeof (r)) 1) << ((rsize) - 1)) \
+ : ((rsigned) > 0 || (r) == 0))) \
+ || ((rsigned) > 0 \
+ && !X##_s \
+ && X##_e == _FP_EXPBIAS_##fs + (rsize) - 2 \
+ && (r) == (((typeof (r)) 1) << ((rsize) - 1)))) \
+ { \
+ if ((rsigned) != 2) \
+ { \
+ if ((rsigned) != 0) \
+ { \
+ (r) = 1; \
+ (r) <<= (rsize) - 1; \
+ (r) -= 1 - X##_s; \
+ } \
+ else \
+ { \
+ (r) = 0; \
+ (r) = ~(r); \
+ } \
+ } \
+ _FP_TO_INT_ROUND_inexact = 0; \
+ FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
+ } \
+ } \
+ if (_FP_TO_INT_ROUND_inexact) \
+ FP_SET_EXCEPTION (FP_EX_INEXACT); \
+ } \
+ _FP_TO_INT_ROUND_done: ; \
+ } \
+ 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 \
+ { \
+ __label__ pack_semiraw; \
+ if (r) \
+ { \
+ rtype _FP_FROM_INT_ur = (r); \
+ \
+ if ((X##_s = ((r) < 0))) \
+ _FP_FROM_INT_ur = -_FP_FROM_INT_ur; \
+ \
+ _FP_STATIC_ASSERT ((rsize) <= 2 * _FP_W_TYPE_SIZE, \
+ "rsize too large"); \
+ (void) (((rsize) <= _FP_W_TYPE_SIZE) \
+ ? ({ \
+ int _FP_FROM_INT_lz; \
+ __FP_CLZ (_FP_FROM_INT_lz, \
+ (_FP_W_TYPE) _FP_FROM_INT_ur); \
+ X##_e = (_FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 \
+ - _FP_FROM_INT_lz); \
+ }) \
+ : ({ \
+ int _FP_FROM_INT_lz; \
+ __FP_CLZ_2 (_FP_FROM_INT_lz, \
+ (_FP_W_TYPE) (_FP_FROM_INT_ur \
+ >> _FP_W_TYPE_SIZE), \
+ (_FP_W_TYPE) _FP_FROM_INT_ur); \
+ X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
+ - _FP_FROM_INT_lz); \
+ })); \
+ \
+ 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, _FP_FROM_INT_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) \
+ _FP_FROM_INT_ur \
+ = ((_FP_FROM_INT_ur >> (X##_e - _FP_EXPBIAS_##fs \
+ - _FP_WFRACBITS_##fs + 1)) \
+ | ((_FP_FROM_INT_ur \
+ << ((rsize) - (X##_e - _FP_EXPBIAS_##fs \
+ - _FP_WFRACBITS_##fs + 1))) \
+ != 0)); \
+ _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_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. If CHECK_NAN, then signaling NaNs are
+ converted to quiet with the "invalid" exception raised; otherwise
+ signaling NaNs remain signaling with no exception. */
+#define _FP_EXTEND_CNAN(dfs, sfs, dwc, swc, D, S, check_nan) \
+ do \
+ { \
+ _FP_STATIC_ASSERT (_FP_FRACBITS_##dfs >= _FP_FRACBITS_##sfs, \
+ "destination mantissa narrower than source"); \
+ _FP_STATIC_ASSERT ((_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \
+ >= _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs), \
+ "destination max exponent smaller" \
+ " than source"); \
+ _FP_STATIC_ASSERT (((_FP_EXPBIAS_##dfs \
+ >= (_FP_EXPBIAS_##sfs \
+ + _FP_FRACBITS_##sfs - 1)) \
+ || (_FP_EXPBIAS_##dfs == _FP_EXPBIAS_##sfs)), \
+ "source subnormals do not all become normal," \
+ " but bias not the same"); \
+ 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) \
+ { \
+ _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
+ 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; \
+ if (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW) \
+ FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
+ } \
+ else \
+ { \
+ int FP_EXTEND_lz; \
+ FP_SET_EXCEPTION (FP_EX_DENORM); \
+ _FP_FRAC_CLZ_##swc (FP_EXTEND_lz, S); \
+ _FP_FRAC_SLL_##dwc (D, \
+ FP_EXTEND_lz + _FP_FRACBITS_##dfs \
+ - _FP_FRACTBITS_##sfs); \
+ D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
+ + _FP_FRACXBITS_##sfs - FP_EXTEND_lz); \
+ } \
+ } \
+ else \
+ { \
+ D##_e = _FP_EXPMAX_##dfs; \
+ if (!_FP_FRAC_ZEROP_##swc (S)) \
+ { \
+ if (check_nan && _FP_FRAC_SNANP (sfs, S)) \
+ FP_SET_EXCEPTION (FP_EX_INVALID \
+ | FP_EX_INVALID_SNAN); \
+ _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
+ - _FP_FRACBITS_##sfs)); \
+ if (check_nan) \
+ _FP_SETQNAN (dfs, dwc, D); \
+ } \
+ } \
+ } \
+ } \
+ while (0)
+
+#define FP_EXTEND(dfs, sfs, dwc, swc, D, S) \
+ _FP_EXTEND_CNAN (dfs, sfs, dwc, swc, D, S, 1)
+
+/* 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 \
+ { \
+ _FP_STATIC_ASSERT (_FP_FRACBITS_##sfs >= _FP_FRACBITS_##dfs, \
+ "destination mantissa wider than source"); \
+ _FP_STATIC_ASSERT (((_FP_EXPBIAS_##sfs \
+ >= (_FP_EXPBIAS_##dfs \
+ + _FP_FRACBITS_##dfs - 1)) \
+ || _FP_EXPBIAS_##sfs == _FP_EXPBIAS_##dfs), \
+ "source subnormals do not all become same," \
+ " but bias not the same"); \
+ 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) \
+ { \
+ _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
+ 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 \
+ { \
+ _FP_STATIC_ASSERT ((sizeof (_FP_W_TYPE) == sizeof (unsigned int) \
+ || (sizeof (_FP_W_TYPE) \
+ == sizeof (unsigned long)) \
+ || (sizeof (_FP_W_TYPE) \
+ == sizeof (unsigned long long))), \
+ "_FP_W_TYPE size unsupported for clz"); \
+ 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 /* sizeof (_FP_W_TYPE) == sizeof (unsigned long long). */ \
+ (r) = __builtin_clzll (x); \
+ } \
+ 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 _FP_DIV_MEAT_N_loop_count = _FP_WFRACBITS_##fs; \
+ _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_u); \
+ _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_v); \
+ _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_u, X); \
+ _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_v, Y); \
+ _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
+ /* Normalize _FP_DIV_MEAT_N_LOOP_U and _FP_DIV_MEAT_N_LOOP_V. */ \
+ _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, _FP_WFRACXBITS_##fs); \
+ _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_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 (_FP_DIV_MEAT_N_loop_u, _FP_DIV_MEAT_N_loop_v)) \
+ { \
+ _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
+ _FP_DIV_MEAT_N_loop_u, \
+ _FP_DIV_MEAT_N_loop_v); \
+ _FP_FRAC_LOW_##wc (R) |= 1; \
+ _FP_DIV_MEAT_N_loop_count--; \
+ } \
+ else \
+ R##_e--; \
+ /* Subsequent rounds. */ \
+ do \
+ { \
+ int _FP_DIV_MEAT_N_loop_msb \
+ = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (_FP_DIV_MEAT_N_loop_u) < 0; \
+ _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, 1); \
+ _FP_FRAC_SLL_##wc (R, 1); \
+ if (_FP_DIV_MEAT_N_loop_msb \
+ || _FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, \
+ _FP_DIV_MEAT_N_loop_v)) \
+ { \
+ _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
+ _FP_DIV_MEAT_N_loop_u, \
+ _FP_DIV_MEAT_N_loop_v); \
+ _FP_FRAC_LOW_##wc (R) |= 1; \
+ } \
+ } \
+ while (--_FP_DIV_MEAT_N_loop_count > 0); \
+ /* If there's anything left in _FP_DIV_MEAT_N_LOOP_U, the result \
+ is inexact. */ \
+ _FP_FRAC_LOW_##wc (R) \
+ |= !_FP_FRAC_ZEROP_##wc (_FP_DIV_MEAT_N_loop_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)
+
+#endif /* !SOFT_FP_OP_COMMON_H */
diff --git a/include/math-emu/quad.h b/include/math-emu/quad.h
new file mode 100644
index 0000000..9b5191c
--- /dev/null
+++ b/include/math-emu/quad.h
@@ -0,0 +1,330 @@
+/* Software floating-point emulation.
+ Definitions for IEEE Quad Precision.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_QUAD_H
+#define SOFT_FP_QUAD_H 1
+
+#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_Q (4*_FP_W_TYPE_SIZE)
+# define _FP_FRACTBITS_DW_Q (8*_FP_W_TYPE_SIZE)
+#else
+# define _FP_FRACTBITS_Q (2*_FP_W_TYPE_SIZE)
+# define _FP_FRACTBITS_DW_Q (4*_FP_W_TYPE_SIZE)
+#endif
+
+#define _FP_FRACBITS_Q 113
+#define _FP_FRACXBITS_Q (_FP_FRACTBITS_Q - _FP_FRACBITS_Q)
+#define _FP_WFRACBITS_Q (_FP_WORKBITS + _FP_FRACBITS_Q)
+#define _FP_WFRACXBITS_Q (_FP_FRACTBITS_Q - _FP_WFRACBITS_Q)
+#define _FP_EXPBITS_Q 15
+#define _FP_EXPBIAS_Q 16383
+#define _FP_EXPMAX_Q 32767
+
+#define _FP_QNANBIT_Q \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_Q-2) % _FP_W_TYPE_SIZE)
+#define _FP_QNANBIT_SH_Q \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_Q-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
+#define _FP_IMPLBIT_Q \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_Q-1) % _FP_W_TYPE_SIZE)
+#define _FP_IMPLBIT_SH_Q \
+ ((_FP_W_TYPE) 1 << (_FP_FRACBITS_Q-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
+#define _FP_OVERFLOW_Q \
+ ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_Q % _FP_W_TYPE_SIZE))
+
+#define _FP_WFRACBITS_DW_Q (2 * _FP_WFRACBITS_Q)
+#define _FP_WFRACXBITS_DW_Q (_FP_FRACTBITS_DW_Q - _FP_WFRACBITS_DW_Q)
+#define _FP_HIGHBIT_DW_Q \
+ ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_Q - 1) % _FP_W_TYPE_SIZE)
+
+typedef float TFtype __attribute__ ((mode (TF)));
+
+#if _FP_W_TYPE_SIZE < 64
+
+union _FP_UNION_Q
+{
+ TFtype flt;
+ struct _FP_STRUCT_LAYOUT
+ {
+# if __BYTE_ORDER == __BIG_ENDIAN
+ unsigned sign : 1;
+ unsigned exp : _FP_EXPBITS_Q;
+ unsigned long frac3 : _FP_FRACBITS_Q - (_FP_IMPLBIT_Q != 0)-(_FP_W_TYPE_SIZE * 3);
+ unsigned long frac2 : _FP_W_TYPE_SIZE;
+ 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 long frac2 : _FP_W_TYPE_SIZE;
+ unsigned long frac3 : _FP_FRACBITS_Q - (_FP_IMPLBIT_Q != 0)-(_FP_W_TYPE_SIZE * 3);
+ unsigned exp : _FP_EXPBITS_Q;
+ unsigned sign : 1;
+# endif /* not bigendian */
+ } bits __attribute__ ((packed));
+};
+
+
+# define FP_DECL_Q(X) _FP_DECL (4, X)
+# define FP_UNPACK_RAW_Q(X, val) _FP_UNPACK_RAW_4 (Q, X, (val))
+# define FP_UNPACK_RAW_QP(X, val) _FP_UNPACK_RAW_4_P (Q, X, (val))
+# define FP_PACK_RAW_Q(val, X) _FP_PACK_RAW_4 (Q, (val), X)
+# define FP_PACK_RAW_QP(val, X) \
+ do \
+ { \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_4_P (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_Q(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_4 (Q, X, (val)); \
+ _FP_UNPACK_CANONICAL (Q, 4, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_QP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_4_P (Q, X, (val)); \
+ _FP_UNPACK_CANONICAL (Q, 4, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_Q(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_4 (Q, X, (val)); \
+ _FP_UNPACK_SEMIRAW (Q, 4, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_QP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_4_P (Q, X, (val)); \
+ _FP_UNPACK_SEMIRAW (Q, 4, X); \
+ } \
+ while (0)
+
+# define FP_PACK_Q(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (Q, 4, X); \
+ _FP_PACK_RAW_4 (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_QP(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (Q, 4, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_4_P (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_Q(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (Q, 4, X); \
+ _FP_PACK_RAW_4 (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_QP(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (Q, 4, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_4_P (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_ISSIGNAN_Q(X) _FP_ISSIGNAN (Q, 4, X)
+# define FP_NEG_Q(R, X) _FP_NEG (Q, 4, R, X)
+# define FP_ADD_Q(R, X, Y) _FP_ADD (Q, 4, R, X, Y)
+# define FP_SUB_Q(R, X, Y) _FP_SUB (Q, 4, R, X, Y)
+# define FP_MUL_Q(R, X, Y) _FP_MUL (Q, 4, R, X, Y)
+# define FP_DIV_Q(R, X, Y) _FP_DIV (Q, 4, R, X, Y)
+# define FP_SQRT_Q(R, X) _FP_SQRT (Q, 4, R, X)
+# define _FP_SQRT_MEAT_Q(R, S, T, X, Q) _FP_SQRT_MEAT_4 (R, S, T, X, (Q))
+# define FP_FMA_Q(R, X, Y, Z) _FP_FMA (Q, 4, 8, R, X, Y, Z)
+
+# define FP_CMP_Q(r, X, Y, un, ex) _FP_CMP (Q, 4, (r), X, Y, (un), (ex))
+# define FP_CMP_EQ_Q(r, X, Y, ex) _FP_CMP_EQ (Q, 4, (r), X, Y, (ex))
+# define FP_CMP_UNORD_Q(r, X, Y, ex) _FP_CMP_UNORD (Q, 4, (r), X, Y, (ex))
+
+# define FP_TO_INT_Q(r, X, rsz, rsg) _FP_TO_INT (Q, 4, (r), X, (rsz), (rsg))
+# define FP_TO_INT_ROUND_Q(r, X, rsz, rsg) \
+ _FP_TO_INT_ROUND (Q, 4, (r), X, (rsz), (rsg))
+# define FP_FROM_INT_Q(X, r, rs, rt) _FP_FROM_INT (Q, 4, X, (r), (rs), rt)
+
+# define _FP_FRAC_HIGH_Q(X) _FP_FRAC_HIGH_4 (X)
+# define _FP_FRAC_HIGH_RAW_Q(X) _FP_FRAC_HIGH_4 (X)
+
+# define _FP_FRAC_HIGH_DW_Q(X) _FP_FRAC_HIGH_8 (X)
+
+#else /* not _FP_W_TYPE_SIZE < 64 */
+union _FP_UNION_Q
+{
+ TFtype flt /* __attribute__ ((mode (TF))) */ ;
+ struct _FP_STRUCT_LAYOUT
+ {
+ _FP_W_TYPE a, b;
+ } longs;
+ struct _FP_STRUCT_LAYOUT
+ {
+# if __BYTE_ORDER == __BIG_ENDIAN
+ unsigned sign : 1;
+ unsigned exp : _FP_EXPBITS_Q;
+ _FP_W_TYPE frac1 : _FP_FRACBITS_Q - (_FP_IMPLBIT_Q != 0) - _FP_W_TYPE_SIZE;
+ _FP_W_TYPE frac0 : _FP_W_TYPE_SIZE;
+# else
+ _FP_W_TYPE frac0 : _FP_W_TYPE_SIZE;
+ _FP_W_TYPE frac1 : _FP_FRACBITS_Q - (_FP_IMPLBIT_Q != 0) - _FP_W_TYPE_SIZE;
+ unsigned exp : _FP_EXPBITS_Q;
+ unsigned sign : 1;
+# endif
+ } bits;
+};
+
+# define FP_DECL_Q(X) _FP_DECL (2, X)
+# define FP_UNPACK_RAW_Q(X, val) _FP_UNPACK_RAW_2 (Q, X, (val))
+# define FP_UNPACK_RAW_QP(X, val) _FP_UNPACK_RAW_2_P (Q, X, (val))
+# define FP_PACK_RAW_Q(val, X) _FP_PACK_RAW_2 (Q, (val), X)
+# define FP_PACK_RAW_QP(val, X) \
+ do \
+ { \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_2_P (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_Q(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2 (Q, X, (val)); \
+ _FP_UNPACK_CANONICAL (Q, 2, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_QP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2_P (Q, X, (val)); \
+ _FP_UNPACK_CANONICAL (Q, 2, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_Q(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2 (Q, X, (val)); \
+ _FP_UNPACK_SEMIRAW (Q, 2, X); \
+ } \
+ while (0)
+
+# define FP_UNPACK_SEMIRAW_QP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_2_P (Q, X, (val)); \
+ _FP_UNPACK_SEMIRAW (Q, 2, X); \
+ } \
+ while (0)
+
+# define FP_PACK_Q(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (Q, 2, X); \
+ _FP_PACK_RAW_2 (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_QP(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (Q, 2, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_2_P (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_Q(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (Q, 2, X); \
+ _FP_PACK_RAW_2 (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_PACK_SEMIRAW_QP(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (Q, 2, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_2_P (Q, (val), X); \
+ } \
+ while (0)
+
+# define FP_ISSIGNAN_Q(X) _FP_ISSIGNAN (Q, 2, X)
+# define FP_NEG_Q(R, X) _FP_NEG (Q, 2, R, X)
+# define FP_ADD_Q(R, X, Y) _FP_ADD (Q, 2, R, X, Y)
+# define FP_SUB_Q(R, X, Y) _FP_SUB (Q, 2, R, X, Y)
+# define FP_MUL_Q(R, X, Y) _FP_MUL (Q, 2, R, X, Y)
+# define FP_DIV_Q(R, X, Y) _FP_DIV (Q, 2, R, X, Y)
+# define FP_SQRT_Q(R, X) _FP_SQRT (Q, 2, R, X)
+# define _FP_SQRT_MEAT_Q(R, S, T, X, Q) _FP_SQRT_MEAT_2 (R, S, T, X, (Q))
+# define FP_FMA_Q(R, X, Y, Z) _FP_FMA (Q, 2, 4, R, X, Y, Z)
+
+# define FP_CMP_Q(r, X, Y, un, ex) _FP_CMP (Q, 2, (r), X, Y, (un), (ex))
+# define FP_CMP_EQ_Q(r, X, Y, ex) _FP_CMP_EQ (Q, 2, (r), X, Y, (ex))
+# define FP_CMP_UNORD_Q(r, X, Y, ex) _FP_CMP_UNORD (Q, 2, (r), X, Y, (ex))
+
+# define FP_TO_INT_Q(r, X, rsz, rsg) _FP_TO_INT (Q, 2, (r), X, (rsz), (rsg))
+# define FP_TO_INT_ROUND_Q(r, X, rsz, rsg) \
+ _FP_TO_INT_ROUND (Q, 2, (r), X, (rsz), (rsg))
+# define FP_FROM_INT_Q(X, r, rs, rt) _FP_FROM_INT (Q, 2, X, (r), (rs), rt)
+
+# define _FP_FRAC_HIGH_Q(X) _FP_FRAC_HIGH_2 (X)
+# define _FP_FRAC_HIGH_RAW_Q(X) _FP_FRAC_HIGH_2 (X)
+
+# define _FP_FRAC_HIGH_DW_Q(X) _FP_FRAC_HIGH_4 (X)
+
+#endif /* not _FP_W_TYPE_SIZE < 64 */
+
+#endif /* !SOFT_FP_QUAD_H */
diff --git a/include/math-emu/single.h b/include/math-emu/single.h
new file mode 100644
index 0000000..b035140
--- /dev/null
+++ b/include/math-emu/single.h
@@ -0,0 +1,199 @@
+/* Software floating-point emulation.
+ Definitions for IEEE Single Precision.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_SINGLE_H
+#define SOFT_FP_SINGLE_H 1
+
+#if _FP_W_TYPE_SIZE < 32
+# error "Here's a nickel kid. Go buy yourself a real computer."
+#endif
+
+#define _FP_FRACTBITS_S _FP_W_TYPE_SIZE
+
+#if _FP_W_TYPE_SIZE < 64
+# define _FP_FRACTBITS_DW_S (2 * _FP_W_TYPE_SIZE)
+#else
+# define _FP_FRACTBITS_DW_S _FP_W_TYPE_SIZE
+#endif
+
+#define _FP_FRACBITS_S 24
+#define _FP_FRACXBITS_S (_FP_FRACTBITS_S - _FP_FRACBITS_S)
+#define _FP_WFRACBITS_S (_FP_WORKBITS + _FP_FRACBITS_S)
+#define _FP_WFRACXBITS_S (_FP_FRACTBITS_S - _FP_WFRACBITS_S)
+#define _FP_EXPBITS_S 8
+#define _FP_EXPBIAS_S 127
+#define _FP_EXPMAX_S 255
+#define _FP_QNANBIT_S ((_FP_W_TYPE) 1 << (_FP_FRACBITS_S-2))
+#define _FP_QNANBIT_SH_S ((_FP_W_TYPE) 1 << (_FP_FRACBITS_S-2+_FP_WORKBITS))
+#define _FP_IMPLBIT_S ((_FP_W_TYPE) 1 << (_FP_FRACBITS_S-1))
+#define _FP_IMPLBIT_SH_S ((_FP_W_TYPE) 1 << (_FP_FRACBITS_S-1+_FP_WORKBITS))
+#define _FP_OVERFLOW_S ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_S))
+
+#define _FP_WFRACBITS_DW_S (2 * _FP_WFRACBITS_S)
+#define _FP_WFRACXBITS_DW_S (_FP_FRACTBITS_DW_S - _FP_WFRACBITS_DW_S)
+#define _FP_HIGHBIT_DW_S \
+ ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_S - 1) % _FP_W_TYPE_SIZE)
+
+/* The implementation of _FP_MUL_MEAT_S and _FP_DIV_MEAT_S should be
+ chosen by the target machine. */
+
+typedef float SFtype __attribute__ ((mode (SF)));
+
+union _FP_UNION_S
+{
+ SFtype flt;
+ struct _FP_STRUCT_LAYOUT
+ {
+#if __BYTE_ORDER == __BIG_ENDIAN
+ unsigned sign : 1;
+ unsigned exp : _FP_EXPBITS_S;
+ unsigned frac : _FP_FRACBITS_S - (_FP_IMPLBIT_S != 0);
+#else
+ unsigned frac : _FP_FRACBITS_S - (_FP_IMPLBIT_S != 0);
+ unsigned exp : _FP_EXPBITS_S;
+ unsigned sign : 1;
+#endif
+ } bits __attribute__ ((packed));
+};
+
+#define FP_DECL_S(X) _FP_DECL (1, X)
+#define FP_UNPACK_RAW_S(X, val) _FP_UNPACK_RAW_1 (S, X, (val))
+#define FP_UNPACK_RAW_SP(X, val) _FP_UNPACK_RAW_1_P (S, X, (val))
+#define FP_PACK_RAW_S(val, X) _FP_PACK_RAW_1 (S, (val), X)
+#define FP_PACK_RAW_SP(val, X) \
+ do \
+ { \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_1_P (S, (val), X); \
+ } \
+ while (0)
+
+#define FP_UNPACK_S(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1 (S, X, (val)); \
+ _FP_UNPACK_CANONICAL (S, 1, X); \
+ } \
+ while (0)
+
+#define FP_UNPACK_SP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1_P (S, X, (val)); \
+ _FP_UNPACK_CANONICAL (S, 1, X); \
+ } \
+ while (0)
+
+#define FP_UNPACK_SEMIRAW_S(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1 (S, X, (val)); \
+ _FP_UNPACK_SEMIRAW (S, 1, X); \
+ } \
+ while (0)
+
+#define FP_UNPACK_SEMIRAW_SP(X, val) \
+ do \
+ { \
+ _FP_UNPACK_RAW_1_P (S, X, (val)); \
+ _FP_UNPACK_SEMIRAW (S, 1, X); \
+ } \
+ while (0)
+
+#define FP_PACK_S(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (S, 1, X); \
+ _FP_PACK_RAW_1 (S, (val), X); \
+ } \
+ while (0)
+
+#define FP_PACK_SP(val, X) \
+ do \
+ { \
+ _FP_PACK_CANONICAL (S, 1, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_1_P (S, (val), X); \
+ } \
+ while (0)
+
+#define FP_PACK_SEMIRAW_S(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (S, 1, X); \
+ _FP_PACK_RAW_1 (S, (val), X); \
+ } \
+ while (0)
+
+#define FP_PACK_SEMIRAW_SP(val, X) \
+ do \
+ { \
+ _FP_PACK_SEMIRAW (S, 1, X); \
+ if (!FP_INHIBIT_RESULTS) \
+ _FP_PACK_RAW_1_P (S, (val), X); \
+ } \
+ while (0)
+
+#define FP_ISSIGNAN_S(X) _FP_ISSIGNAN (S, 1, X)
+#define FP_NEG_S(R, X) _FP_NEG (S, 1, R, X)
+#define FP_ADD_S(R, X, Y) _FP_ADD (S, 1, R, X, Y)
+#define FP_SUB_S(R, X, Y) _FP_SUB (S, 1, R, X, Y)
+#define FP_MUL_S(R, X, Y) _FP_MUL (S, 1, R, X, Y)
+#define FP_DIV_S(R, X, Y) _FP_DIV (S, 1, R, X, Y)
+#define FP_SQRT_S(R, X) _FP_SQRT (S, 1, R, X)
+#define _FP_SQRT_MEAT_S(R, S, T, X, Q) _FP_SQRT_MEAT_1 (R, S, T, X, (Q))
+
+#if _FP_W_TYPE_SIZE < 64
+# define FP_FMA_S(R, X, Y, Z) _FP_FMA (S, 1, 2, R, X, Y, Z)
+#else
+# define FP_FMA_S(R, X, Y, Z) _FP_FMA (S, 1, 1, R, X, Y, Z)
+#endif
+
+#define FP_CMP_S(r, X, Y, un, ex) _FP_CMP (S, 1, (r), X, Y, (un), (ex))
+#define FP_CMP_EQ_S(r, X, Y, ex) _FP_CMP_EQ (S, 1, (r), X, Y, (ex))
+#define FP_CMP_UNORD_S(r, X, Y, ex) _FP_CMP_UNORD (S, 1, (r), X, Y, (ex))
+
+#define FP_TO_INT_S(r, X, rsz, rsg) _FP_TO_INT (S, 1, (r), X, (rsz), (rsg))
+#define FP_TO_INT_ROUND_S(r, X, rsz, rsg) \
+ _FP_TO_INT_ROUND (S, 1, (r), X, (rsz), (rsg))
+#define FP_FROM_INT_S(X, r, rs, rt) _FP_FROM_INT (S, 1, X, (r), (rs), rt)
+
+#define _FP_FRAC_HIGH_S(X) _FP_FRAC_HIGH_1 (X)
+#define _FP_FRAC_HIGH_RAW_S(X) _FP_FRAC_HIGH_1 (X)
+
+#if _FP_W_TYPE_SIZE < 64
+# define _FP_FRAC_HIGH_DW_S(X) _FP_FRAC_HIGH_2 (X)
+#else
+# define _FP_FRAC_HIGH_DW_S(X) _FP_FRAC_HIGH_1 (X)
+#endif
+
+#endif /* !SOFT_FP_SINGLE_H */
diff --git a/include/math-emu/soft-fp.h b/include/math-emu/soft-fp.h
new file mode 100644
index 0000000..3b39336
--- /dev/null
+++ b/include/math-emu/soft-fp.h
@@ -0,0 +1,354 @@
+/* Software floating-point emulation.
+ Copyright (C) 1997-2015 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Richard Henderson (rth@xxxxxxxxxx),
+ Jakub Jelinek (jj@xxxxxxxxxxxxxx),
+ David S. Miller (davem@xxxxxxxxxx) and
+ Peter Maydell (pmaydell@xxxxxxxxxxxxxxxxxxxxxx).
+
+ 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/>. */
+
+#ifndef SOFT_FP_H
+#define SOFT_FP_H 1
+
+#ifdef _LIBC
+# include <sfp-machine.h>
+#elif defined __KERNEL__
+/* The Linux kernel uses asm/ names for architecture-specific
+ files. */
+# include <asm/sfp-machine.h>
+#else
+# include "sfp-machine.h"
+#endif
+
+/* Allow sfp-machine to have its own byte order definitions. */
+#ifndef __BYTE_ORDER
+# ifdef _LIBC
+# include <endian.h>
+# else
+# error "endianness not defined by sfp-machine.h"
+# endif
+#endif
+
+/* For unreachable default cases in switch statements over bitwise OR
+ of FP_CLS_* values. */
+#if (defined __GNUC__ \
+ && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 5)))
+# define _FP_UNREACHABLE __builtin_unreachable ()
+#else
+# define _FP_UNREACHABLE abort ()
+#endif
+
+#if ((defined __GNUC__ \
+ && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))) \
+ || (defined __STDC_VERSION__ && __STDC_VERSION__ >= 201112L))
+# define _FP_STATIC_ASSERT(expr, msg) \
+ _Static_assert ((expr), msg)
+#else
+# define _FP_STATIC_ASSERT(expr, msg) \
+ extern int (*__Static_assert_function (void)) \
+ [!!sizeof (struct { int __error_if_negative: (expr) ? 2 : -1; })]
+#endif
+
+/* In the Linux kernel, some architectures have a single function that
+ uses different kinds of unpacking and packing depending on the
+ instruction being emulated, meaning it is not readily visible to
+ the compiler that variables from _FP_DECL and _FP_FRAC_DECL_*
+ macros are only used in cases where they were initialized. */
+#ifdef __KERNEL__
+# define _FP_ZERO_INIT = 0
+#else
+# define _FP_ZERO_INIT
+#endif
+
+#define _FP_WORKBITS 3
+#define _FP_WORK_LSB ((_FP_W_TYPE) 1 << 3)
+#define _FP_WORK_ROUND ((_FP_W_TYPE) 1 << 2)
+#define _FP_WORK_GUARD ((_FP_W_TYPE) 1 << 1)
+#define _FP_WORK_STICKY ((_FP_W_TYPE) 1 << 0)
+
+#ifndef FP_RND_NEAREST
+# define FP_RND_NEAREST 0
+# define FP_RND_ZERO 1
+# define FP_RND_PINF 2
+# define FP_RND_MINF 3
+#endif
+#ifndef FP_ROUNDMODE
+# define FP_ROUNDMODE FP_RND_NEAREST
+#endif
+
+/* By default don't care about exceptions. */
+#ifndef FP_EX_INVALID
+# define FP_EX_INVALID 0
+#endif
+#ifndef FP_EX_OVERFLOW
+# define FP_EX_OVERFLOW 0
+#endif
+#ifndef FP_EX_UNDERFLOW
+# define FP_EX_UNDERFLOW 0
+#endif
+#ifndef FP_EX_DIVZERO
+# define FP_EX_DIVZERO 0
+#endif
+#ifndef FP_EX_INEXACT
+# define FP_EX_INEXACT 0
+#endif
+#ifndef FP_EX_DENORM
+# define FP_EX_DENORM 0
+#endif
+
+/* Sub-exceptions of "invalid". */
+/* Signaling NaN operand. */
+#ifndef FP_EX_INVALID_SNAN
+# define FP_EX_INVALID_SNAN 0
+#endif
+/* Inf * 0. */
+#ifndef FP_EX_INVALID_IMZ
+# define FP_EX_INVALID_IMZ 0
+#endif
+/* fma (Inf, 0, c). */
+#ifndef FP_EX_INVALID_IMZ_FMA
+# define FP_EX_INVALID_IMZ_FMA 0
+#endif
+/* Inf - Inf. */
+#ifndef FP_EX_INVALID_ISI
+# define FP_EX_INVALID_ISI 0
+#endif
+/* 0 / 0. */
+#ifndef FP_EX_INVALID_ZDZ
+# define FP_EX_INVALID_ZDZ 0
+#endif
+/* Inf / Inf. */
+#ifndef FP_EX_INVALID_IDI
+# define FP_EX_INVALID_IDI 0
+#endif
+/* sqrt (negative). */
+#ifndef FP_EX_INVALID_SQRT
+# define FP_EX_INVALID_SQRT 0
+#endif
+/* Invalid conversion to integer. */
+#ifndef FP_EX_INVALID_CVI
+# define FP_EX_INVALID_CVI 0
+#endif
+/* Invalid comparison. */
+#ifndef FP_EX_INVALID_VC
+# define FP_EX_INVALID_VC 0
+#endif
+
+/* _FP_STRUCT_LAYOUT may be defined as an attribute to determine the
+ struct layout variant used for structures where bit-fields are used
+ to access specific parts of binary floating-point numbers. This is
+ required for systems where the default ABI uses struct layout with
+ differences in how consecutive bit-fields are laid out from the
+ default expected by soft-fp. */
+#ifndef _FP_STRUCT_LAYOUT
+# define _FP_STRUCT_LAYOUT
+#endif
+
+#ifdef _FP_DECL_EX
+# define FP_DECL_EX \
+ int _fex = 0; \
+ _FP_DECL_EX
+#else
+# define FP_DECL_EX int _fex = 0
+#endif
+
+/* Initialize any machine-specific state used in FP_ROUNDMODE,
+ FP_TRAPPING_EXCEPTIONS or FP_HANDLE_EXCEPTIONS. */
+#ifndef FP_INIT_ROUNDMODE
+# define FP_INIT_ROUNDMODE do {} while (0)
+#endif
+
+/* Initialize any machine-specific state used in
+ FP_TRAPPING_EXCEPTIONS or FP_HANDLE_EXCEPTIONS. */
+#ifndef FP_INIT_TRAPPING_EXCEPTIONS
+# define FP_INIT_TRAPPING_EXCEPTIONS FP_INIT_ROUNDMODE
+#endif
+
+/* Initialize any machine-specific state used in
+ FP_HANDLE_EXCEPTIONS. */
+#ifndef FP_INIT_EXCEPTIONS
+# define FP_INIT_EXCEPTIONS FP_INIT_TRAPPING_EXCEPTIONS
+#endif
+
+#ifndef FP_HANDLE_EXCEPTIONS
+# define FP_HANDLE_EXCEPTIONS do {} while (0)
+#endif
+
+/* Whether to flush subnormal inputs to zero with the same sign. */
+#ifndef FP_DENORM_ZERO
+# define FP_DENORM_ZERO 0
+#endif
+
+#ifndef FP_INHIBIT_RESULTS
+/* By default we write the results always.
+ sfp-machine may override this and e.g.
+ check if some exceptions are unmasked
+ and inhibit it in such a case. */
+# define FP_INHIBIT_RESULTS 0
+#endif
+
+#define FP_SET_EXCEPTION(ex) \
+ _fex |= (ex)
+
+#define FP_CUR_EXCEPTIONS \
+ (_fex)
+
+#ifndef FP_TRAPPING_EXCEPTIONS
+# define FP_TRAPPING_EXCEPTIONS 0
+#endif
+
+/* A file using soft-fp may define FP_NO_EXCEPTIONS before including
+ soft-fp.h to indicate that, although a macro used there could raise
+ exceptions, or do rounding and potentially thereby raise
+ exceptions, for some arguments, for the particular arguments used
+ in that file no exceptions or rounding can occur. Such a file
+ should not itself use macros relating to handling exceptions and
+ rounding modes; this is only for indirect uses (in particular, in
+ _FP_FROM_INT and the macros it calls). */
+#ifdef FP_NO_EXCEPTIONS
+
+# undef FP_SET_EXCEPTION
+# define FP_SET_EXCEPTION(ex) do {} while (0)
+
+# undef FP_CUR_EXCEPTIONS
+# define FP_CUR_EXCEPTIONS 0
+
+# undef FP_TRAPPING_EXCEPTIONS
+# define FP_TRAPPING_EXCEPTIONS 0
+
+# undef FP_ROUNDMODE
+# define FP_ROUNDMODE FP_RND_ZERO
+
+# undef _FP_TININESS_AFTER_ROUNDING
+# define _FP_TININESS_AFTER_ROUNDING 0
+
+#endif
+
+/* A file using soft-fp may define FP_NO_EXACT_UNDERFLOW before
+ including soft-fp.h to indicate that, although a macro used there
+ could allow for the case of exact underflow requiring the underflow
+ exception to be raised if traps are enabled, for the particular
+ arguments used in that file no exact underflow can occur. */
+#ifdef FP_NO_EXACT_UNDERFLOW
+# undef FP_TRAPPING_EXCEPTIONS
+# define FP_TRAPPING_EXCEPTIONS 0
+#endif
+
+#define _FP_ROUND_NEAREST(wc, X) \
+ do \
+ { \
+ if ((_FP_FRAC_LOW_##wc (X) & 15) != _FP_WORK_ROUND) \
+ _FP_FRAC_ADDI_##wc (X, _FP_WORK_ROUND); \
+ } \
+ while (0)
+
+#define _FP_ROUND_ZERO(wc, X) (void) 0
+
+#define _FP_ROUND_PINF(wc, X) \
+ do \
+ { \
+ if (!X##_s && (_FP_FRAC_LOW_##wc (X) & 7)) \
+ _FP_FRAC_ADDI_##wc (X, _FP_WORK_LSB); \
+ } \
+ while (0)
+
+#define _FP_ROUND_MINF(wc, X) \
+ do \
+ { \
+ if (X##_s && (_FP_FRAC_LOW_##wc (X) & 7)) \
+ _FP_FRAC_ADDI_##wc (X, _FP_WORK_LSB); \
+ } \
+ while (0)
+
+#define _FP_ROUND(wc, X) \
+ do \
+ { \
+ if (_FP_FRAC_LOW_##wc (X) & 7) \
+ { \
+ FP_SET_EXCEPTION (FP_EX_INEXACT); \
+ switch (FP_ROUNDMODE) \
+ { \
+ case FP_RND_NEAREST: \
+ _FP_ROUND_NEAREST (wc, X); \
+ break; \
+ case FP_RND_ZERO: \
+ _FP_ROUND_ZERO (wc, X); \
+ break; \
+ case FP_RND_PINF: \
+ _FP_ROUND_PINF (wc, X); \
+ break; \
+ case FP_RND_MINF: \
+ _FP_ROUND_MINF (wc, X); \
+ break; \
+ } \
+ } \
+ } \
+ while (0)
+
+#define FP_CLS_NORMAL 0
+#define FP_CLS_ZERO 1
+#define FP_CLS_INF 2
+#define FP_CLS_NAN 3
+
+#define _FP_CLS_COMBINE(x, y) (((x) << 2) | (y))
+
+#include "op-1.h"
+#include "op-2.h"
+#include "op-4.h"
+#include "op-8.h"
+#include "op-common.h"
+
+/* Sigh. Silly things longlong.h needs. */
+#define UWtype _FP_W_TYPE
+#define W_TYPE_SIZE _FP_W_TYPE_SIZE
+
+typedef int QItype __attribute__ ((mode (QI)));
+typedef int SItype __attribute__ ((mode (SI)));
+typedef int DItype __attribute__ ((mode (DI)));
+typedef unsigned int UQItype __attribute__ ((mode (QI)));
+typedef unsigned int USItype __attribute__ ((mode (SI)));
+typedef unsigned int UDItype __attribute__ ((mode (DI)));
+#if _FP_W_TYPE_SIZE == 32
+typedef unsigned int UHWtype __attribute__ ((mode (HI)));
+#elif _FP_W_TYPE_SIZE == 64
+typedef USItype UHWtype;
+#endif
+
+#ifndef CMPtype
+# define CMPtype int
+#endif
+
+#define SI_BITS (__CHAR_BIT__ * (int) sizeof (SItype))
+#define DI_BITS (__CHAR_BIT__ * (int) sizeof (DItype))
+
+#ifndef umul_ppmm
+# ifdef _LIBC
+# include <stdlib/longlong.h>
+# else
+# include "longlong.h"
+# endif
+#endif
+
+#endif /* !SOFT_FP_H */

--
Joseph S. Myers
joseph@xxxxxxxxxxxxxxxx
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