cachepc-linux

Fork of AMDESE/linux with modifications for CachePC side-channel attack
git clone https://git.sinitax.com/sinitax/cachepc-linux
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op-2.h (20190B)


      1/* Software floating-point emulation.
      2   Basic two-word fraction declaration and manipulation.
      3   Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
      4   This file is part of the GNU C Library.
      5   Contributed by Richard Henderson (rth@cygnus.com),
      6		  Jakub Jelinek (jj@ultra.linux.cz),
      7		  David S. Miller (davem@redhat.com) and
      8		  Peter Maydell (pmaydell@chiark.greenend.org.uk).
      9
     10   The GNU C Library is free software; you can redistribute it and/or
     11   modify it under the terms of the GNU Library General Public License as
     12   published by the Free Software Foundation; either version 2 of the
     13   License, or (at your option) any later version.
     14
     15   The GNU C Library is distributed in the hope that it will be useful,
     16   but WITHOUT ANY WARRANTY; without even the implied warranty of
     17   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
     18   Library General Public License for more details.
     19
     20   You should have received a copy of the GNU Library General Public
     21   License along with the GNU C Library; see the file COPYING.LIB.  If
     22   not, write to the Free Software Foundation, Inc.,
     23   59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
     24
     25#ifndef __MATH_EMU_OP_2_H__
     26#define __MATH_EMU_OP_2_H__
     27
     28#define _FP_FRAC_DECL_2(X)	_FP_W_TYPE X##_f0 = 0, X##_f1 = 0
     29#define _FP_FRAC_COPY_2(D,S)	(D##_f0 = S##_f0, D##_f1 = S##_f1)
     30#define _FP_FRAC_SET_2(X,I)	__FP_FRAC_SET_2(X, I)
     31#define _FP_FRAC_HIGH_2(X)	(X##_f1)
     32#define _FP_FRAC_LOW_2(X)	(X##_f0)
     33#define _FP_FRAC_WORD_2(X,w)	(X##_f##w)
     34#define _FP_FRAC_SLL_2(X, N) (						       \
     35	(void) (((N) < _FP_W_TYPE_SIZE)					       \
     36	  ? ({								       \
     37		if (__builtin_constant_p(N) && (N) == 1) {		       \
     38			X##_f1 = X##_f1 + X##_f1 +			       \
     39				(((_FP_WS_TYPE) (X##_f0)) < 0);		       \
     40			X##_f0 += X##_f0;				       \
     41		} else {						       \
     42			X##_f1 = X##_f1 << (N) | X##_f0 >>		       \
     43						(_FP_W_TYPE_SIZE - (N));       \
     44			X##_f0 <<= (N);					       \
     45		}							       \
     46		0;							       \
     47	    })								       \
     48	  : ({								       \
     49	      X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE);		       \
     50	      X##_f0 = 0;						       \
     51	  })))
     52
     53
     54#define _FP_FRAC_SRL_2(X, N) (						       \
     55	(void) (((N) < _FP_W_TYPE_SIZE)					       \
     56	  ? ({								       \
     57	      X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N));      \
     58	      X##_f1 >>= (N);						       \
     59	    })								       \
     60	  : ({								       \
     61	      X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE);		       \
     62	      X##_f1 = 0;						       \
     63	    })))
     64
     65
     66/* Right shift with sticky-lsb.  */
     67#define _FP_FRAC_SRS_2(X, N, sz) (					       \
     68	(void) (((N) < _FP_W_TYPE_SIZE)					       \
     69	  ? ({								       \
     70	      X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)      \
     71			| (__builtin_constant_p(N) && (N) == 1		       \
     72			   ? X##_f0 & 1					       \
     73			   : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0));       \
     74		X##_f1 >>= (N);						       \
     75	    })								       \
     76	  : ({								       \
     77	      X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)		       \
     78			| ((((N) == _FP_W_TYPE_SIZE			       \
     79			     ? 0					       \
     80			     : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N))))          \
     81			    | X##_f0) != 0));				       \
     82	      X##_f1 = 0;						       \
     83	    })))
     84
     85#define _FP_FRAC_ADDI_2(X,I)	\
     86  __FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
     87
     88#define _FP_FRAC_ADD_2(R,X,Y)	\
     89  __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
     90
     91#define _FP_FRAC_SUB_2(R,X,Y)	\
     92  __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
     93
     94#define _FP_FRAC_DEC_2(X,Y)	\
     95  __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0)
     96
     97#define _FP_FRAC_CLZ_2(R,X)	\
     98  do {				\
     99    if (X##_f1)			\
    100      __FP_CLZ(R,X##_f1);	\
    101    else 			\
    102    {				\
    103      __FP_CLZ(R,X##_f0);	\
    104      R += _FP_W_TYPE_SIZE;	\
    105    }				\
    106  } while(0)
    107
    108/* Predicates */
    109#define _FP_FRAC_NEGP_2(X)	((_FP_WS_TYPE)X##_f1 < 0)
    110#define _FP_FRAC_ZEROP_2(X)	((X##_f1 | X##_f0) == 0)
    111#define _FP_FRAC_OVERP_2(fs,X)	(_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
    112#define _FP_FRAC_CLEAR_OVERP_2(fs,X)	(_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
    113#define _FP_FRAC_EQ_2(X, Y)	(X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
    114#define _FP_FRAC_GT_2(X, Y)	\
    115  (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
    116#define _FP_FRAC_GE_2(X, Y)	\
    117  (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
    118
    119#define _FP_ZEROFRAC_2		0, 0
    120#define _FP_MINFRAC_2		0, 1
    121#define _FP_MAXFRAC_2		(~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
    122
    123/*
    124 * Internals 
    125 */
    126
    127#define __FP_FRAC_SET_2(X,I1,I0)	(X##_f0 = I0, X##_f1 = I1)
    128
    129#define __FP_CLZ_2(R, xh, xl)	\
    130  do {				\
    131    if (xh)			\
    132      __FP_CLZ(R,xh);		\
    133    else 			\
    134    {				\
    135      __FP_CLZ(R,xl);		\
    136      R += _FP_W_TYPE_SIZE;	\
    137    }				\
    138  } while(0)
    139
    140#if 0
    141
    142#ifndef __FP_FRAC_ADDI_2
    143#define __FP_FRAC_ADDI_2(xh, xl, i)	\
    144  (xh += ((xl += i) < i))
    145#endif
    146#ifndef __FP_FRAC_ADD_2
    147#define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl)	\
    148  (rh = xh + yh + ((rl = xl + yl) < xl))
    149#endif
    150#ifndef __FP_FRAC_SUB_2
    151#define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl)	\
    152  (rh = xh - yh - ((rl = xl - yl) > xl))
    153#endif
    154#ifndef __FP_FRAC_DEC_2
    155#define __FP_FRAC_DEC_2(xh, xl, yh, yl)	\
    156  do {					\
    157    UWtype _t = xl;			\
    158    xh -= yh + ((xl -= yl) > _t);	\
    159  } while (0)
    160#endif
    161
    162#else
    163
    164#undef __FP_FRAC_ADDI_2
    165#define __FP_FRAC_ADDI_2(xh, xl, i)	add_ssaaaa(xh, xl, xh, xl, 0, i)
    166#undef __FP_FRAC_ADD_2
    167#define __FP_FRAC_ADD_2			add_ssaaaa
    168#undef __FP_FRAC_SUB_2
    169#define __FP_FRAC_SUB_2			sub_ddmmss
    170#undef __FP_FRAC_DEC_2
    171#define __FP_FRAC_DEC_2(xh, xl, yh, yl)	sub_ddmmss(xh, xl, xh, xl, yh, yl)
    172
    173#endif
    174
    175/*
    176 * Unpack the raw bits of a native fp value.  Do not classify or
    177 * normalize the data.
    178 */
    179
    180#define _FP_UNPACK_RAW_2(fs, X, val)			\
    181  do {							\
    182    union _FP_UNION_##fs _flo; _flo.flt = (val);	\
    183							\
    184    X##_f0 = _flo.bits.frac0;				\
    185    X##_f1 = _flo.bits.frac1;				\
    186    X##_e  = _flo.bits.exp;				\
    187    X##_s  = _flo.bits.sign;				\
    188  } while (0)
    189
    190#define _FP_UNPACK_RAW_2_P(fs, X, val)			\
    191  do {							\
    192    union _FP_UNION_##fs *_flo =			\
    193      (union _FP_UNION_##fs *)(val);			\
    194							\
    195    X##_f0 = _flo->bits.frac0;				\
    196    X##_f1 = _flo->bits.frac1;				\
    197    X##_e  = _flo->bits.exp;				\
    198    X##_s  = _flo->bits.sign;				\
    199  } while (0)
    200
    201
    202/*
    203 * Repack the raw bits of a native fp value.
    204 */
    205
    206#define _FP_PACK_RAW_2(fs, val, X)			\
    207  do {							\
    208    union _FP_UNION_##fs _flo;				\
    209							\
    210    _flo.bits.frac0 = X##_f0;				\
    211    _flo.bits.frac1 = X##_f1;				\
    212    _flo.bits.exp   = X##_e;				\
    213    _flo.bits.sign  = X##_s;				\
    214							\
    215    (val) = _flo.flt;					\
    216  } while (0)
    217
    218#define _FP_PACK_RAW_2_P(fs, val, X)			\
    219  do {							\
    220    union _FP_UNION_##fs *_flo =			\
    221      (union _FP_UNION_##fs *)(val);			\
    222							\
    223    _flo->bits.frac0 = X##_f0;				\
    224    _flo->bits.frac1 = X##_f1;				\
    225    _flo->bits.exp   = X##_e;				\
    226    _flo->bits.sign  = X##_s;				\
    227  } while (0)
    228
    229
    230/*
    231 * Multiplication algorithms:
    232 */
    233
    234/* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
    235
    236#define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit)			\
    237  do {									\
    238    _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);	\
    239									\
    240    doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0);	\
    241    doit(_b_f1, _b_f0, X##_f0, Y##_f1);					\
    242    doit(_c_f1, _c_f0, X##_f1, Y##_f0);					\
    243    doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1);	\
    244									\
    245    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    246		    _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0,		\
    247		    _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    248		    _FP_FRAC_WORD_4(_z,1));				\
    249    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    250		    _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0,		\
    251		    _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    252		    _FP_FRAC_WORD_4(_z,1));				\
    253									\
    254    /* Normalize since we know where the msb of the multiplicands	\
    255       were (bit B), we know that the msb of the of the product is	\
    256       at either 2B or 2B-1.  */					\
    257    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);			\
    258    R##_f0 = _FP_FRAC_WORD_4(_z,0);					\
    259    R##_f1 = _FP_FRAC_WORD_4(_z,1);					\
    260  } while (0)
    261
    262/* Given a 1W * 1W => 2W primitive, do the extended multiplication.
    263   Do only 3 multiplications instead of four. This one is for machines
    264   where multiplication is much more expensive than subtraction.  */
    265
    266#define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit)		\
    267  do {									\
    268    _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);	\
    269    _FP_W_TYPE _d;							\
    270    int _c1, _c2;							\
    271									\
    272    _b_f0 = X##_f0 + X##_f1;						\
    273    _c1 = _b_f0 < X##_f0;						\
    274    _b_f1 = Y##_f0 + Y##_f1;						\
    275    _c2 = _b_f1 < Y##_f0;						\
    276    doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0);			\
    277    doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1);	\
    278    doit(_c_f1, _c_f0, X##_f1, Y##_f1);					\
    279									\
    280    _b_f0 &= -_c2;							\
    281    _b_f1 &= -_c1;							\
    282    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    283		    _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d,		\
    284		    0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1));	\
    285    __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    286		     _b_f0);						\
    287    __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    288		     _b_f1);						\
    289    __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    290		    _FP_FRAC_WORD_4(_z,1),				\
    291		    0, _d, _FP_FRAC_WORD_4(_z,0));			\
    292    __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
    293		    _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0);		\
    294    __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2),	\
    295		    _c_f1, _c_f0,					\
    296		    _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2));	\
    297									\
    298    /* Normalize since we know where the msb of the multiplicands	\
    299       were (bit B), we know that the msb of the of the product is	\
    300       at either 2B or 2B-1.  */					\
    301    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);			\
    302    R##_f0 = _FP_FRAC_WORD_4(_z,0);					\
    303    R##_f1 = _FP_FRAC_WORD_4(_z,1);					\
    304  } while (0)
    305
    306#define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y)				\
    307  do {									\
    308    _FP_FRAC_DECL_4(_z);						\
    309    _FP_W_TYPE _x[2], _y[2];						\
    310    _x[0] = X##_f0; _x[1] = X##_f1;					\
    311    _y[0] = Y##_f0; _y[1] = Y##_f1;					\
    312									\
    313    mpn_mul_n(_z_f, _x, _y, 2);						\
    314									\
    315    /* Normalize since we know where the msb of the multiplicands	\
    316       were (bit B), we know that the msb of the of the product is	\
    317       at either 2B or 2B-1.  */					\
    318    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);			\
    319    R##_f0 = _z_f[0];							\
    320    R##_f1 = _z_f[1];							\
    321  } while (0)
    322
    323/* Do at most 120x120=240 bits multiplication using double floating
    324   point multiplication.  This is useful if floating point
    325   multiplication has much bigger throughput than integer multiply.
    326   It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
    327   between 106 and 120 only.  
    328   Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
    329   SETFETZ is a macro which will disable all FPU exceptions and set rounding
    330   towards zero,  RESETFE should optionally reset it back.  */
    331
    332#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe)	\
    333  do {										\
    334    static const double _const[] = {						\
    335      /* 2^-24 */ 5.9604644775390625e-08,					\
    336      /* 2^-48 */ 3.5527136788005009e-15,					\
    337      /* 2^-72 */ 2.1175823681357508e-22,					\
    338      /* 2^-96 */ 1.2621774483536189e-29,					\
    339      /* 2^28 */ 2.68435456e+08,						\
    340      /* 2^4 */ 1.600000e+01,							\
    341      /* 2^-20 */ 9.5367431640625e-07,						\
    342      /* 2^-44 */ 5.6843418860808015e-14,					\
    343      /* 2^-68 */ 3.3881317890172014e-21,					\
    344      /* 2^-92 */ 2.0194839173657902e-28,					\
    345      /* 2^-116 */ 1.2037062152420224e-35};					\
    346    double _a240, _b240, _c240, _d240, _e240, _f240, 				\
    347	   _g240, _h240, _i240, _j240, _k240;					\
    348    union { double d; UDItype i; } _l240, _m240, _n240, _o240,			\
    349				   _p240, _q240, _r240, _s240;			\
    350    UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0;			\
    351										\
    352    if (wfracbits < 106 || wfracbits > 120)					\
    353      abort();									\
    354										\
    355    setfetz;									\
    356										\
    357    _e240 = (double)(long)(X##_f0 & 0xffffff);					\
    358    _j240 = (double)(long)(Y##_f0 & 0xffffff);					\
    359    _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff);				\
    360    _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff);				\
    361    _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48));	\
    362    _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48));	\
    363    _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff);				\
    364    _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff);				\
    365    _a240 = (double)(long)(X##_f1 >> 32);					\
    366    _f240 = (double)(long)(Y##_f1 >> 32);					\
    367    _e240 *= _const[3];								\
    368    _j240 *= _const[3];								\
    369    _d240 *= _const[2];								\
    370    _i240 *= _const[2];								\
    371    _c240 *= _const[1];								\
    372    _h240 *= _const[1];								\
    373    _b240 *= _const[0];								\
    374    _g240 *= _const[0];								\
    375    _s240.d =							      _e240*_j240;\
    376    _r240.d =						_d240*_j240 + _e240*_i240;\
    377    _q240.d =				  _c240*_j240 + _d240*_i240 + _e240*_h240;\
    378    _p240.d =		    _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\
    379    _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\
    380    _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240;		\
    381    _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240;				\
    382    _l240.d = _a240*_g240 + _b240*_f240;					\
    383    _k240 =   _a240*_f240;							\
    384    _r240.d += _s240.d;								\
    385    _q240.d += _r240.d;								\
    386    _p240.d += _q240.d;								\
    387    _o240.d += _p240.d;								\
    388    _n240.d += _o240.d;								\
    389    _m240.d += _n240.d;								\
    390    _l240.d += _m240.d;								\
    391    _k240 += _l240.d;								\
    392    _s240.d -= ((_const[10]+_s240.d)-_const[10]);				\
    393    _r240.d -= ((_const[9]+_r240.d)-_const[9]);					\
    394    _q240.d -= ((_const[8]+_q240.d)-_const[8]);					\
    395    _p240.d -= ((_const[7]+_p240.d)-_const[7]);					\
    396    _o240.d += _const[7];							\
    397    _n240.d += _const[6];							\
    398    _m240.d += _const[5];							\
    399    _l240.d += _const[4];							\
    400    if (_s240.d != 0.0) _y240 = 1;						\
    401    if (_r240.d != 0.0) _y240 = 1;						\
    402    if (_q240.d != 0.0) _y240 = 1;						\
    403    if (_p240.d != 0.0) _y240 = 1;						\
    404    _t240 = (DItype)_k240;							\
    405    _u240 = _l240.i;								\
    406    _v240 = _m240.i;								\
    407    _w240 = _n240.i;								\
    408    _x240 = _o240.i;								\
    409    R##_f1 = (_t240 << (128 - (wfracbits - 1)))					\
    410	     | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104));			\
    411    R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1)))			\
    412    	     | ((_v240 & 0xffffff) << (144 - (wfracbits - 1)))			\
    413    	     | ((_w240 & 0xffffff) << (120 - (wfracbits - 1)))			\
    414    	     | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96))			\
    415    	     | _y240;								\
    416    resetfe;									\
    417  } while (0)
    418
    419/*
    420 * Division algorithms:
    421 */
    422
    423#define _FP_DIV_MEAT_2_udiv(fs, R, X, Y)				\
    424  do {									\
    425    _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0;		\
    426    if (_FP_FRAC_GT_2(X, Y))						\
    427      {									\
    428	_n_f2 = X##_f1 >> 1;						\
    429	_n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1;		\
    430	_n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1);			\
    431      }									\
    432    else								\
    433      {									\
    434	R##_e--;							\
    435	_n_f2 = X##_f1;							\
    436	_n_f1 = X##_f0;							\
    437	_n_f0 = 0;							\
    438      }									\
    439									\
    440    /* Normalize, i.e. make the most significant bit of the 		\
    441       denominator set. */						\
    442    _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs);				\
    443									\
    444    udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1);			\
    445    umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0);				\
    446    _r_f0 = _n_f0;							\
    447    if (_FP_FRAC_GT_2(_m, _r))						\
    448      {									\
    449	R##_f1--;							\
    450	_FP_FRAC_ADD_2(_r, Y, _r);					\
    451	if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r))		\
    452	  {								\
    453	    R##_f1--;							\
    454	    _FP_FRAC_ADD_2(_r, Y, _r);					\
    455	  }								\
    456      }									\
    457    _FP_FRAC_DEC_2(_r, _m);						\
    458									\
    459    if (_r_f1 == Y##_f1)						\
    460      {									\
    461	/* This is a special case, not an optimization			\
    462	   (_r/Y##_f1 would not fit into UWtype).			\
    463	   As _r is guaranteed to be < Y,  R##_f0 can be either		\
    464	   (UWtype)-1 or (UWtype)-2.  But as we know what kind		\
    465	   of bits it is (sticky, guard, round),  we don't care.	\
    466	   We also don't care what the reminder is,  because the	\
    467	   guard bit will be set anyway.  -jj */			\
    468	R##_f0 = -1;							\
    469      }									\
    470    else								\
    471      {									\
    472	udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1);		\
    473	umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0);			\
    474	_r_f0 = 0;							\
    475	if (_FP_FRAC_GT_2(_m, _r))					\
    476	  {								\
    477	    R##_f0--;							\
    478	    _FP_FRAC_ADD_2(_r, Y, _r);					\
    479	    if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r))		\
    480	      {								\
    481		R##_f0--;						\
    482		_FP_FRAC_ADD_2(_r, Y, _r);				\
    483	      }								\
    484	  }								\
    485	if (!_FP_FRAC_EQ_2(_r, _m))					\
    486	  R##_f0 |= _FP_WORK_STICKY;					\
    487      }									\
    488  } while (0)
    489
    490
    491#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y)					\
    492  do {									\
    493    _FP_W_TYPE _x[4], _y[2], _z[4];					\
    494    _y[0] = Y##_f0; _y[1] = Y##_f1;					\
    495    _x[0] = _x[3] = 0;							\
    496    if (_FP_FRAC_GT_2(X, Y))						\
    497      {									\
    498	R##_e++;							\
    499	_x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) |	\
    500		 X##_f1 >> (_FP_W_TYPE_SIZE -				\
    501			    (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE)));	\
    502	_x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE);	\
    503      }									\
    504    else								\
    505      {									\
    506	_x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) |	\
    507		 X##_f1 >> (_FP_W_TYPE_SIZE -				\
    508			    (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE)));	\
    509	_x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE);	\
    510      }									\
    511									\
    512    (void) mpn_divrem (_z, 0, _x, 4, _y, 2);				\
    513    R##_f1 = _z[1];							\
    514    R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0);				\
    515  } while (0)
    516
    517
    518/*
    519 * Square root algorithms:
    520 * We have just one right now, maybe Newton approximation
    521 * should be added for those machines where division is fast.
    522 */
    523 
    524#define _FP_SQRT_MEAT_2(R, S, T, X, q)			\
    525  do {							\
    526    while (q)						\
    527      {							\
    528	T##_f1 = S##_f1 + q;				\
    529	if (T##_f1 <= X##_f1)				\
    530	  {						\
    531	    S##_f1 = T##_f1 + q;			\
    532	    X##_f1 -= T##_f1;				\
    533	    R##_f1 += q;				\
    534	  }						\
    535	_FP_FRAC_SLL_2(X, 1);				\
    536	q >>= 1;					\
    537      }							\
    538    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);		\
    539    while (q != _FP_WORK_ROUND)				\
    540      {							\
    541	T##_f0 = S##_f0 + q;				\
    542	T##_f1 = S##_f1;				\
    543	if (T##_f1 < X##_f1 || 				\
    544	    (T##_f1 == X##_f1 && T##_f0 <= X##_f0))	\
    545	  {						\
    546	    S##_f0 = T##_f0 + q;			\
    547	    S##_f1 += (T##_f0 > S##_f0);		\
    548	    _FP_FRAC_DEC_2(X, T);			\
    549	    R##_f0 += q;				\
    550	  }						\
    551	_FP_FRAC_SLL_2(X, 1);				\
    552	q >>= 1;					\
    553      }							\
    554    if (X##_f0 | X##_f1)				\
    555      {							\
    556	if (S##_f1 < X##_f1 || 				\
    557	    (S##_f1 == X##_f1 && S##_f0 < X##_f0))	\
    558	  R##_f0 |= _FP_WORK_ROUND;			\
    559	R##_f0 |= _FP_WORK_STICKY;			\
    560      }							\
    561  } while (0)
    562
    563
    564/*
    565 * Assembly/disassembly for converting to/from integral types.  
    566 * No shifting or overflow handled here.
    567 */
    568
    569#define _FP_FRAC_ASSEMBLE_2(r, X, rsize)	\
    570	(void) (((rsize) <= _FP_W_TYPE_SIZE)	\
    571		? ({ (r) = X##_f0; })		\
    572		: ({				\
    573		     (r) = X##_f1;		\
    574		     (r) <<= _FP_W_TYPE_SIZE;	\
    575		     (r) += X##_f0;		\
    576		    }))
    577
    578#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize)				\
    579  do {									\
    580    X##_f0 = r;								\
    581    X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE);	\
    582  } while (0)
    583
    584/*
    585 * Convert FP values between word sizes
    586 */
    587
    588#define _FP_FRAC_CONV_1_2(dfs, sfs, D, S)				\
    589  do {									\
    590    if (S##_c != FP_CLS_NAN)						\
    591      _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),	\
    592		     _FP_WFRACBITS_##sfs);				\
    593    else								\
    594      _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));	\
    595    D##_f = S##_f0;							\
    596  } while (0)
    597
    598#define _FP_FRAC_CONV_2_1(dfs, sfs, D, S)				\
    599  do {									\
    600    D##_f0 = S##_f;							\
    601    D##_f1 = 0;								\
    602    _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));	\
    603  } while (0)
    604
    605#endif