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/* Software floating-point emulation. |
Basic one-word fraction declaration and manipulation. |
Copyright (C) 1997,1998,1999,2006 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, write to the Free |
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, |
MA 02110-1301, USA. */ |
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#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) |
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#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) |
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/* 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) |
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#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) |
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#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))) |
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#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) |
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/* 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) |
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#define _FP_ZEROFRAC_1 0 |
#define _FP_MINFRAC_1 1 |
#define _FP_MAXFRAC_1 (~(_FP_WS_TYPE)0) |
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/* |
* 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) |
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#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) |
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/* |
* 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) |
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#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) |
|
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/* |
* Multiplication algorithms: |
*/ |
|
/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the |
multiplication immediately. */ |
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#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) |
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/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ |
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#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) |
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/* Finally, a simple widening multiply algorithm. What fun! */ |
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#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) |
|
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/* |
* 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) |
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/* 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. */ |
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#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) |
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#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) |
|
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/* |
* Square root algorithms: |
* We have just one right now, maybe Newton approximation |
* should be added for those machines where division is fast. |
*/ |
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#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) |
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/* |
* Assembly/disassembly for converting to/from integral types. |
* No shifting or overflow handled here. |
*/ |
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#define _FP_FRAC_ASSEMBLE_1(r, X, rsize) (r = X##_f) |
#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = r) |
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/* |
* Convert FP values between word sizes |
*/ |
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#define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f) |