You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
397 lines
11 KiB
397 lines
11 KiB
20 years ago
|
/* 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__ */
|