/* Software floating-point emulation.
Definitions for IEEE Extended Precision.
Copyright (C) 1999 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek (jj@ultra.linux.cz).
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If
not, write to the Free Software Foundation, Inc.,
59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
#ifndef __MATH_EMU_EXTENDED_H__
#define __MATH_EMU_EXTENDED_H__
#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_E (4*_FP_W_TYPE_SIZE)
#else
#define _FP_FRACTBITS_E (2*_FP_W_TYPE_SIZE)
#endif
#define _FP_FRACBITS_E 64
#define _FP_FRACXBITS_E (_FP_FRACTBITS_E - _FP_FRACBITS_E)
#define _FP_WFRACBITS_E (_FP_WORKBITS + _FP_FRACBITS_E)
#define _FP_WFRACXBITS_E (_FP_FRACTBITS_E - _FP_WFRACBITS_E)
#define _FP_EXPBITS_E 15
#define _FP_EXPBIAS_E 16383
#define _FP_EXPMAX_E 32767
#define _FP_QNANBIT_E \
((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE)
#define _FP_IMPLBIT_E \
((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE)
#define _FP_OVERFLOW_E \
((_FP_W_TYPE)1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE))
#if _FP_W_TYPE_SIZE < 64
union _FP_UNION_E
{
long double flt;
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned long pad1 : _FP_W_TYPE_SIZE;
unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
unsigned long sign : 1;
unsigned long exp : _FP_EXPBITS_E;
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 exp : _FP_EXPBITS_E;
unsigned sign : 1;
#endif /* not bigendian */
} bits __attribute__((packed));
};
#define FP_DECL_E(X) _FP_DECL(4,X)
#define FP_UNPACK_RAW_E(X, val) \
do { \
union _FP_UNION_E _flo; _flo.flt = (val); \
\
X##_f[2] = 0; X##_f[3] = 0; \
X##_f[0] = _flo.bits.frac0; \
X##_f[1] = _flo.bits.frac1; \
X##_e = _flo.bits.exp; \
X##_s = _flo.bits.sign; \
if (!X##_e && (X##_f[1] || X##_f[0]) \
&& !(X##_f[1] & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_UNPACK_RAW_EP(X, val) \
do { \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
X##_f[2] = 0; X##_f[3] = 0; \
X##_f[0] = _flo->bits.frac0; \
X##_f[1] = _flo->bits.frac1; \
X##_e = _flo->bits.exp; \
X##_s = _flo->bits.sign; \
if (!X##_e && (X##_f[1] || X##_f[0]) \
&& !(X##_f[1] & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_PACK_RAW_E(val, X) \
do { \
union _FP_UNION_E _flo; \
\
if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
else X##_f[1] &= ~(_FP_IMPLBIT_E); \
_flo.bits.frac0 = X##_f[0]; \
_flo.bits.frac1 = X##_f[1]; \
_flo.bits.exp = X##_e; \
_flo.bits.sign = X##_s; \
\
(val) = _flo.flt; \
} while (0)
#define FP_PACK_RAW_EP(val, X) \
do { \
if (!FP_INHIBIT_RESULTS) \
{ \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
else X##_f[1] &= ~(_FP_IMPLBIT_E); \
_flo->bits.frac0 = X##_f[0]; \
_flo->bits.frac1 = X##_f[1]; \
_flo->bits.exp = X##_e; \
_flo->bits.sign = X##_s; \
} \
} while (0)
#define FP_UNPACK_E(X,val) \
do { \
FP_UNPACK_RAW_E(X,val); \
_FP_UNPACK_CANONICAL(E,4,X); \
} while (0)
#define FP_UNPACK_EP(X,val) \
do { \
FP_UNPACK_RAW_2_P(X,val); \
_FP_UNPACK_CANONICAL(E,4,X); \
} while (0)
#define FP_PACK_E(val,X) \
do { \
_FP_PACK_CANONICAL(E,4,X); \
FP_PACK_RAW_E(val,X); \
} while (0)
#define FP_PACK_EP(val,X) \
do { \
_FP_PACK_CANONICAL(E,4,X); \
FP_PACK_RAW_EP(val,X); \
} while (0)
#define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,4,X)
#define FP_NEG_E(R,X) _FP_NEG(E,4,R,X)
#define FP_ADD_E(R,X,Y) _FP_ADD(E,4,R,X,Y)
#define FP_SUB_E(R,X,Y) _FP_SUB(E,4,R,X,Y)
#define FP_MUL_E(R,X,Y) _FP_MUL(E,4,R,X,Y)
#define FP_DIV_E(R,X,Y) _FP_DIV(E,4,R,X,Y)
#define FP_SQRT_E(R,X) _FP_SQRT(E,4,R,X)
/*
* Square root algorithms:
* We have just one right now, maybe Newton approximation
* should be added for those machines where division is fast.
* This has special _E version because standard _4 square
* root would not work (it has to start normally with the
* second word and not the first), but as we have to do it
* anyway, we optimize it by doing most of the calculations
* in two UWtype registers instead of four.
*/
#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
do { \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
_FP_FRAC_SRL_4(X, (_FP_WORKBITS)); \
while (q) \
{ \
T##_f[1] = S##_f[1] + q; \
if (T##_f[1] <= X##_f[1]) \
{ \
S##_f[1] = T##_f[1] + q; \
X##_f[1] -= T##_f[1]; \
R##_f[1] += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
while (q) \
{ \
T##_f[0] = S##_f[0] + q; \
T##_f[1] = S##_f[1]; \
if (T##_f[1] < X##_f[1] || \
(T##_f[1] == X##_f[1] && \
T##_f[0] <= X##_f[0])) \
{ \
S##_f[0] = T##_f[0] + q; \
S##_f[1] += (T##_f[0] > S##_f[0]); \
_FP_FRAC_DEC_2(X, T); \
R##_f[0] += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
_FP_FRAC_SLL_4(R, (_FP_WORKBITS)); \
if (X##_f[0] | X##_f[1]) \
{ \
if (S##_f[1] < X##_f[1] || \
(S##_f[1] == X##_f[1] && \
S##_f[0] < X##_f[0])) \
R##_f[0] |= _FP_WORK_ROUND; \
R##_f[0] |= _FP_WORK_STICKY; \
} \
} while (0)
#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,4,r,X,Y,un)
#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,4,r,X,Y)
#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,4,r,X,rsz,rsg)
#define FP_TO_INT_ROUND_E(r,X,rsz,rsg) _FP_TO_INT_ROUND(E,4,r,X,rsz,rsg)
#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,4,X,r,rs,rt)
#define _FP_FRAC_HIGH_E(X) (X##_f[2])
#define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1])
#else /* not _FP_W_TYPE_SIZE < 64 */
union _FP_UNION_E
{
long double flt /* __attribute__((mode(TF))) */ ;
struct {
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned long pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
unsigned sign : 1;
unsigned exp : _FP_EXPBITS_E;
unsigned long frac : _FP_W_TYPE_SIZE;
#else
unsigned long frac : _FP_W_TYPE_SIZE;
unsigned exp : _FP_EXPBITS_E;
unsigned sign : 1;
#endif
} bits;
};
#define FP_DECL_E(X) _FP_DECL(2,X)
#define FP_UNPACK_RAW_E(X, val) \
do { \
union _FP_UNION_E _flo; _flo.flt = (val); \
\
X##_f0 = _flo.bits.frac; \
X##_f1 = 0; \
X##_e = _flo.bits.exp; \
X##_s = _flo.bits.sign; \
if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_UNPACK_RAW_EP(X, val) \
do { \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
X##_f0 = _flo->bits.frac; \
X##_f1 = 0; \
X##_e = _flo->bits.exp; \
X##_s = _flo->bits.sign; \
if (!X##_e && X##_f0 && !(X##_f0 & _FP_IMPLBIT_E)) \
{ \
X##_e++; \
FP_SET_EXCEPTION(FP_EX_DENORM); \
} \
} while (0)
#define FP_PACK_RAW_E(val, X) \
do { \
union _FP_UNION_E _flo; \
\
if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
else X##_f0 &= ~(_FP_IMPLBIT_E); \
_flo.bits.frac = X##_f0; \
_flo.bits.exp = X##_e; \
_flo.bits.sign = X##_s; \
\
(val) = _flo.flt; \
} while (0)
#define FP_PACK_RAW_EP(fs, val, X) \
do { \
if (!FP_INHIBIT_RESULTS) \
{ \
union _FP_UNION_E *_flo = \
(union _FP_UNION_E *)(val); \
\
if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
else X##_f0 &= ~(_FP_IMPLBIT_E); \
_flo->bits.frac = X##_f0; \
_flo->bits.exp = X##_e; \
_flo->bits.sign = X##_s; \
} \
} while (0)
#define FP_UNPACK_E(X,val) \
do { \
FP_UNPACK_RAW_E(X,val); \
_FP_UNPACK_CANONICAL(E,2,X); \
} while (0)
#define FP_UNPACK_EP(X,val) \
do { \
FP_UNPACK_RAW_EP(X,val); \
_FP_UNPACK_CANONICAL(E,2,X); \
} while (0)
#define FP_PACK_E(val,X) \
do { \
_FP_PACK_CANONICAL(E,2,X); \
FP_PACK_RAW_E(val,X); \
} while (0)
#define FP_PACK_EP(val,X) \
do { \
_FP_PACK_CANONICAL(E,2,X); \
FP_PACK_RAW_EP(val,X); \
} while (0)
#define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,2,X)
#define FP_NEG_E(R,X) _FP_NEG(E,2,R,X)
#define FP_ADD_E(R,X,Y) _FP_ADD(E,2,R,X,Y)
#define FP_SUB_E(R,X,Y) _FP_SUB(E,2,R,X,Y)
#define FP_MUL_E(R,X,Y) _FP_MUL(E,2,R,X,Y)
#define FP_DIV_E(R,X,Y) _FP_DIV(E,2,R,X,Y)
#define FP_SQRT_E(R,X) _FP_SQRT(E,2,R,X)
/*
* Square root algorithms:
* We have just one right now, maybe Newton approximation
* should be added for those machines where division is fast.
* We optimize it by doing most of the calculations
* in one UWtype registers instead of two, although we don't
* have to.
*/
#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
do { \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
_FP_FRAC_SRL_2(X, (_FP_WORKBITS)); \
while (q) \
{ \
T##_f0 = S##_f0 + q; \
if (T##_f0 <= X##_f0) \
{ \
S##_f0 = T##_f0 + q; \
X##_f0 -= T##_f0; \
R##_f0 += q; \
} \
_FP_FRAC_SLL_1(X, 1); \
q >>= 1; \
} \
_FP_FRAC_SLL_2(R, (_FP_WORKBITS)); \
if (X##_f0) \
{ \
if (S##_f0 < X##_f0) \
R##_f0 |= _FP_WORK_ROUND; \
R##_f0 |= _FP_WORK_STICKY; \
} \
} while (0)
#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,2,r,X,Y,un)
#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,2,r,X,Y)
#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,2,r,X,rsz,rsg)
#define FP_TO_INT_ROUND_E(r,X,rsz,rsg) _FP_TO_INT_ROUND(E,2,r,X,rsz,rsg)
#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,2,X,r,rs,rt)
#define _FP_FRAC_HIGH_E(X) (X##_f1)
#define _FP_FRAC_HIGH_RAW_E(X) (X##_f0)
#endif /* not _FP_W_TYPE_SIZE < 64 */
#endif /* __MATH_EMU_EXTENDED_H__ */
