302 lines
9.4 KiB
C
302 lines
9.4 KiB
C
/* Software floating-point emulation.
|
|
Basic one-word fraction declaration and manipulation.
|
|
Copyright (C) 1997-2013 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
Contributed by Richard Henderson (rth@cygnus.com),
|
|
Jakub Jelinek (jj@ultra.linux.cz),
|
|
David S. Miller (davem@redhat.com) and
|
|
Peter Maydell (pmaydell@chiark.greenend.org.uk).
|
|
|
|
The GNU C Library is free software; you can redistribute it and/or
|
|
modify it under the terms of the GNU Lesser General Public
|
|
License as published by the Free Software Foundation; either
|
|
version 2.1 of the License, or (at your option) any later version.
|
|
|
|
In addition to the permissions in the GNU Lesser General Public
|
|
License, the Free Software Foundation gives you unlimited
|
|
permission to link the compiled version of this file into
|
|
combinations with other programs, and to distribute those
|
|
combinations without any restriction coming from the use of this
|
|
file. (The Lesser General Public License restrictions do apply in
|
|
other respects; for example, they cover modification of the file,
|
|
and distribution when not linked into a combine executable.)
|
|
|
|
The GNU C Library is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
Lesser General Public License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public
|
|
License along with the GNU C Library; if not, see
|
|
<http://www.gnu.org/licenses/>. */
|
|
|
|
#define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f
|
|
#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_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 _flo; _flo.flt = (val); \
|
|
\
|
|
X##_f = _flo.bits.frac; \
|
|
X##_e = _flo.bits.exp; \
|
|
X##_s = _flo.bits.sign; \
|
|
} while (0)
|
|
|
|
#define _FP_UNPACK_RAW_1_P(fs, X, val) \
|
|
do { \
|
|
union _FP_UNION_##fs *_flo = \
|
|
(union _FP_UNION_##fs *)(val); \
|
|
\
|
|
X##_f = _flo->bits.frac; \
|
|
X##_e = _flo->bits.exp; \
|
|
X##_s = _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 _flo; \
|
|
\
|
|
_flo.bits.frac = X##_f; \
|
|
_flo.bits.exp = X##_e; \
|
|
_flo.bits.sign = X##_s; \
|
|
\
|
|
(val) = _flo.flt; \
|
|
} while (0)
|
|
|
|
#define _FP_PACK_RAW_1_P(fs, val, X) \
|
|
do { \
|
|
union _FP_UNION_##fs *_flo = \
|
|
(union _FP_UNION_##fs *)(val); \
|
|
\
|
|
_flo->bits.frac = X##_f; \
|
|
_flo->bits.exp = X##_e; \
|
|
_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_1_imm(wfracbits, R, X, Y) \
|
|
do { \
|
|
R##_f = X##_f * Y##_f; \
|
|
/* 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_1_wide(wfracbits, R, X, Y, doit) \
|
|
do { \
|
|
_FP_W_TYPE _Z_f0, _Z_f1; \
|
|
doit(_Z_f1, _Z_f0, X##_f, Y##_f); \
|
|
/* 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(_Z, wfracbits-1, 2*wfracbits); \
|
|
R##_f = _Z_f0; \
|
|
} while (0)
|
|
|
|
/* Finally, a simple widening multiply algorithm. What fun! */
|
|
|
|
#define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \
|
|
do { \
|
|
_FP_W_TYPE _xh, _xl, _yh, _yl, _z_f0, _z_f1, _a_f0, _a_f1; \
|
|
\
|
|
/* split the words in half */ \
|
|
_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \
|
|
_xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \
|
|
_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \
|
|
_yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1); \
|
|
\
|
|
/* multiply the pieces */ \
|
|
_z_f0 = _xl * _yl; \
|
|
_a_f0 = _xh * _yl; \
|
|
_a_f1 = _xl * _yh; \
|
|
_z_f1 = _xh * _yh; \
|
|
\
|
|
/* reassemble into two full words */ \
|
|
if ((_a_f0 += _a_f1) < _a_f1) \
|
|
_z_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2); \
|
|
_a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2); \
|
|
_a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2); \
|
|
_FP_FRAC_ADD_2(_z, _z, _a); \
|
|
\
|
|
/* normalize */ \
|
|
_FP_FRAC_SRS_2(_z, wfracbits - 1, 2*wfracbits); \
|
|
R##_f = _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 _q, _r; \
|
|
X##_f <<= (X##_f < Y##_f \
|
|
? R##_e--, _FP_WFRACBITS_##fs \
|
|
: _FP_WFRACBITS_##fs - 1); \
|
|
doit(_q, _r, X##_f, Y##_f); \
|
|
R##_f = _q | (_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 _nh, _nl, _q, _r, _y; \
|
|
\
|
|
/* Normalize Y -- i.e. make the most significant bit set. */ \
|
|
_y = Y##_f << _FP_WFRACXBITS_##fs; \
|
|
\
|
|
/* Shift X op correspondingly high, that is, up one full word. */ \
|
|
if (X##_f < Y##_f) \
|
|
{ \
|
|
R##_e--; \
|
|
_nl = 0; \
|
|
_nh = X##_f; \
|
|
} \
|
|
else \
|
|
{ \
|
|
_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \
|
|
_nh = X##_f >> 1; \
|
|
} \
|
|
\
|
|
udiv_qrnnd(_q, _r, _nh, _nl, _y); \
|
|
R##_f = _q | (_r != 0); \
|
|
} while (0)
|
|
|
|
#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \
|
|
do { \
|
|
_FP_W_TYPE _nh, _nl, _q, _r; \
|
|
if (X##_f < Y##_f) \
|
|
{ \
|
|
R##_e--; \
|
|
_nl = X##_f << _FP_WFRACBITS_##fs; \
|
|
_nh = X##_f >> _FP_WFRACXBITS_##fs; \
|
|
} \
|
|
else \
|
|
{ \
|
|
_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \
|
|
_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \
|
|
} \
|
|
udiv_qrnnd(_q, _r, _nh, _nl, Y##_f); \
|
|
R##_f = _q | (_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)
|