CoCalc -- op-4.h

GitHub Repository: torvalds/linux
Path: blob/master/include/math-emu/op-4.h
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/* Software floating-point emulation.
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   Basic four-word fraction declaration and manipulation.
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   Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
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   This file is part of the GNU C Library.
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   Contributed by Richard Henderson ([email protected]),
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		  Jakub Jelinek ([email protected]),
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		  David S. Miller ([email protected]) and
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		  Peter Maydell ([email protected]).
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   The GNU C Library is free software; you can redistribute it and/or
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   modify it under the terms of the GNU Library General Public License as
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   published by the Free Software Foundation; either version 2 of the
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   License, or (at your option) any later version.
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   The GNU C Library is distributed in the hope that it will be useful,
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   but WITHOUT ANY WARRANTY; without even the implied warranty of
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   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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   Library General Public License for more details.
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   You should have received a copy of the GNU Library General Public
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   License along with the GNU C Library; see the file COPYING.LIB.  If
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   not, write to the Free Software Foundation, Inc.,
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   59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
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#ifndef __MATH_EMU_OP_4_H__
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#define __MATH_EMU_OP_4_H__
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#define _FP_FRAC_DECL_4(X)	_FP_W_TYPE X##_f[4]
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#define _FP_FRAC_COPY_4(D,S)			\
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  (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1],	\
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   D##_f[2] = S##_f[2], D##_f[3] = S##_f[3])
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#define _FP_FRAC_SET_4(X,I)	__FP_FRAC_SET_4(X, I)
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#define _FP_FRAC_HIGH_4(X)	(X##_f[3])
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#define _FP_FRAC_LOW_4(X)	(X##_f[0])
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#define _FP_FRAC_WORD_4(X,w)	(X##_f[w])
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#define _FP_FRAC_SLL_4(X,N)						\
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  do {									\
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    _FP_I_TYPE _up, _down, _skip, _i;					\
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    _skip = (N) / _FP_W_TYPE_SIZE;					\
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    _up = (N) % _FP_W_TYPE_SIZE;					\
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    _down = _FP_W_TYPE_SIZE - _up;					\
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    if (!_up)								\
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      for (_i = 3; _i >= _skip; --_i)					\
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	X##_f[_i] = X##_f[_i-_skip];					\
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    else								\
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      {									\
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	for (_i = 3; _i > _skip; --_i)					\
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	  X##_f[_i] = X##_f[_i-_skip] << _up				\
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		      | X##_f[_i-_skip-1] >> _down;			\
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	X##_f[_i--] = X##_f[0] << _up; 					\
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      }									\
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    for (; _i >= 0; --_i)						\
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      X##_f[_i] = 0;							\
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  } while (0)
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/* This one was broken too */
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#define _FP_FRAC_SRL_4(X,N)						\
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  do {									\
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    _FP_I_TYPE _up, _down, _skip, _i;					\
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    _skip = (N) / _FP_W_TYPE_SIZE;					\
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    _down = (N) % _FP_W_TYPE_SIZE;					\
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    _up = _FP_W_TYPE_SIZE - _down;					\
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    if (!_down)								\
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      for (_i = 0; _i <= 3-_skip; ++_i)					\
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	X##_f[_i] = X##_f[_i+_skip];					\
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    else								\
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      {									\
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	for (_i = 0; _i < 3-_skip; ++_i)				\
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	  X##_f[_i] = X##_f[_i+_skip] >> _down				\
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		      | X##_f[_i+_skip+1] << _up;			\
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	X##_f[_i++] = X##_f[3] >> _down;				\
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      }									\
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    for (; _i < 4; ++_i)						\
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      X##_f[_i] = 0;							\
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  } while (0)
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/* Right shift with sticky-lsb. 
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 * What this actually means is that we do a standard right-shift,
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 * but that if any of the bits that fall off the right hand side
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 * were one then we always set the LSbit.
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 */
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#define _FP_FRAC_SRS_4(X,N,size)					\
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  do {									\
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    _FP_I_TYPE _up, _down, _skip, _i;					\
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    _FP_W_TYPE _s;							\
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    _skip = (N) / _FP_W_TYPE_SIZE;					\
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    _down = (N) % _FP_W_TYPE_SIZE;					\
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    _up = _FP_W_TYPE_SIZE - _down;					\
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    for (_s = _i = 0; _i < _skip; ++_i)					\
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      _s |= X##_f[_i];							\
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    _s |= X##_f[_i] << _up;						\
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/* s is now != 0 if we want to set the LSbit */				\
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    if (!_down)								\
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      for (_i = 0; _i <= 3-_skip; ++_i)					\
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	X##_f[_i] = X##_f[_i+_skip];					\
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    else								\
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      {									\
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	for (_i = 0; _i < 3-_skip; ++_i)				\
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	  X##_f[_i] = X##_f[_i+_skip] >> _down				\
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		      | X##_f[_i+_skip+1] << _up;			\
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	X##_f[_i++] = X##_f[3] >> _down;				\
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      }									\
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    for (; _i < 4; ++_i)						\
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      X##_f[_i] = 0;							\
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    /* don't fix the LSB until the very end when we're sure f[0] is stable */	\
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    X##_f[0] |= (_s != 0);						\
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  } while (0)
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#define _FP_FRAC_ADD_4(R,X,Y)						\
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  __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0],		\
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		  X##_f[3], X##_f[2], X##_f[1], X##_f[0],		\
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		  Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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#define _FP_FRAC_SUB_4(R,X,Y)						\
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  __FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0],		\
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		  X##_f[3], X##_f[2], X##_f[1], X##_f[0],		\
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		  Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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#define _FP_FRAC_DEC_4(X,Y)						\
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  __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],		\
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		  Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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#define _FP_FRAC_ADDI_4(X,I)						\
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  __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
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#define _FP_ZEROFRAC_4  0,0,0,0
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#define _FP_MINFRAC_4   0,0,0,1
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#define _FP_MAXFRAC_4	(~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
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#define _FP_FRAC_ZEROP_4(X)     ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
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#define _FP_FRAC_NEGP_4(X)      ((_FP_WS_TYPE)X##_f[3] < 0)
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#define _FP_FRAC_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
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#define _FP_FRAC_CLEAR_OVERP_4(fs,X)  (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
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#define _FP_FRAC_EQ_4(X,Y)				\
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 (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1]		\
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  && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
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#define _FP_FRAC_GT_4(X,Y)				\
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 (X##_f[3] > Y##_f[3] ||				\
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  (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||	\
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   (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||	\
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    (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0])	\
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   ))							\
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  ))							\
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 )
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#define _FP_FRAC_GE_4(X,Y)				\
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 (X##_f[3] > Y##_f[3] ||				\
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  (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] ||	\
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   (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] ||	\
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    (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0])	\
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   ))							\
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  ))							\
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 )
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#define _FP_FRAC_CLZ_4(R,X)		\
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  do {					\
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    if (X##_f[3])			\
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    {					\
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	__FP_CLZ(R,X##_f[3]);		\
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    }					\
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    else if (X##_f[2])			\
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    {					\
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	__FP_CLZ(R,X##_f[2]);		\
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	R += _FP_W_TYPE_SIZE;		\
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    }					\
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    else if (X##_f[1])			\
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    {					\
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	__FP_CLZ(R,X##_f[2]);		\
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	R += _FP_W_TYPE_SIZE*2;		\
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    }					\
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    else				\
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    {					\
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	__FP_CLZ(R,X##_f[0]);		\
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	R += _FP_W_TYPE_SIZE*3;		\
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    }					\
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  } while(0)
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#define _FP_UNPACK_RAW_4(fs, X, val)				\
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  do {								\
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    union _FP_UNION_##fs _flo; _flo.flt = (val);		\
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    X##_f[0] = _flo.bits.frac0;					\
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    X##_f[1] = _flo.bits.frac1;					\
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    X##_f[2] = _flo.bits.frac2;					\
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    X##_f[3] = _flo.bits.frac3;					\
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    X##_e  = _flo.bits.exp;					\
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    X##_s  = _flo.bits.sign;					\
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  } while (0)
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#define _FP_UNPACK_RAW_4_P(fs, X, val)				\
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  do {								\
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    union _FP_UNION_##fs *_flo =				\
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      (union _FP_UNION_##fs *)(val);				\
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								\
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    X##_f[0] = _flo->bits.frac0;				\
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    X##_f[1] = _flo->bits.frac1;				\
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    X##_f[2] = _flo->bits.frac2;				\
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    X##_f[3] = _flo->bits.frac3;				\
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    X##_e  = _flo->bits.exp;					\
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    X##_s  = _flo->bits.sign;					\
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  } while (0)
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#define _FP_PACK_RAW_4(fs, val, X)				\
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  do {								\
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    union _FP_UNION_##fs _flo;					\
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    _flo.bits.frac0 = X##_f[0];					\
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    _flo.bits.frac1 = X##_f[1];					\
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    _flo.bits.frac2 = X##_f[2];					\
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    _flo.bits.frac3 = X##_f[3];					\
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    _flo.bits.exp   = X##_e;					\
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    _flo.bits.sign  = X##_s;					\
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    (val) = _flo.flt;				   		\
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  } while (0)
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#define _FP_PACK_RAW_4_P(fs, val, X)				\
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  do {								\
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    union _FP_UNION_##fs *_flo =				\
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      (union _FP_UNION_##fs *)(val);				\
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								\
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    _flo->bits.frac0 = X##_f[0];				\
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    _flo->bits.frac1 = X##_f[1];				\
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    _flo->bits.frac2 = X##_f[2];				\
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    _flo->bits.frac3 = X##_f[3];				\
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    _flo->bits.exp   = X##_e;					\
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    _flo->bits.sign  = X##_s;					\
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  } while (0)
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/*
234
 * Multiplication algorithms:
235
 */
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/* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
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#define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit)			    \
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  do {									    \
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    _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);	    \
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    _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f);	    \
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									    \
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    doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \
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    doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]);				    \
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    doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]);				    \
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    doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]);				    \
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    doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]);				    \
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    doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]);				    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),	    \
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		    _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0,		    \
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		    0,0,_FP_FRAC_WORD_8(_z,1));				    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),	    \
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		    _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0,		    \
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		    _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2),	    \
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		    _FP_FRAC_WORD_8(_z,1));				    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),	    \
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		    _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0,		    \
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		    0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2));	    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),	    \
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		    _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0,		    \
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		    _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),	    \
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		    _FP_FRAC_WORD_8(_z,2));				    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),	    \
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		    _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0,		    \
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		    _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3),	    \
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		    _FP_FRAC_WORD_8(_z,2));				    \
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    doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]);				    \
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    doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]);				    \
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    doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]);				    \
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    doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]);				    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),	    \
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		    _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0,		    \
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		    0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3));	    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),	    \
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		    _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0,		    \
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		    _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),	    \
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		    _FP_FRAC_WORD_8(_z,3));				    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),	    \
280
		    _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0,		    \
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		    _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),	    \
282
		    _FP_FRAC_WORD_8(_z,3));				    \
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    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),	    \
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		    _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0,		    \
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		    _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4),	    \
286
		    _FP_FRAC_WORD_8(_z,3));				    \
287
    doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]);				    \
288
    doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]);				    \
289
    doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]);				    \
290
    doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]);				    \
291
    doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]);				    \
292
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),	    \
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		    _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0,		    \
294
		    0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4));	    \
295
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),	    \
296
		    _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0,		    \
297
		    _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),	    \
298
		    _FP_FRAC_WORD_8(_z,4));				    \
299
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),	    \
300
		    _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0,		    \
301
		    _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5),	    \
302
		    _FP_FRAC_WORD_8(_z,4));				    \
303
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),	    \
304
		    _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0,		    \
305
		    0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5));	    \
306
    __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),	    \
307
		    _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0,		    \
308
		    _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),	    \
309
		    _FP_FRAC_WORD_8(_z,5));				    \
310
    doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]);				    \
311
    __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6),	    \
312
		    _b_f1,_b_f0,					    \
313
		    _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6));	    \
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_8(_z, wfracbits-1, 2*wfracbits);			    \
319
    __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),	    \
320
		    _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));	    \
321
  } while (0)
322

323
#define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y)				    \
324
  do {									    \
325
    _FP_FRAC_DECL_8(_z);						    \
326
									    \
327
    mpn_mul_n(_z_f, _x_f, _y_f, 4);					    \
328
									    \
329
    /* Normalize since we know where the msb of the multiplicands	    \
330
       were (bit B), we know that the msb of the of the product is	    \
331
       at either 2B or 2B-1.  */					    \
332
    _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits);	 		    \
333
    __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2),	    \
334
		    _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0));	    \
335
  } while (0)
336

337
/*
338
 * Helper utility for _FP_DIV_MEAT_4_udiv:
339
 * pppp = m * nnn
340
 */
341
#define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0)				    \
342
  do {									    \
343
    UWtype _t;								    \
344
    umul_ppmm(p1,p0,m,n0);						    \
345
    umul_ppmm(p2,_t,m,n1);						    \
346
    __FP_FRAC_ADDI_2(p2,p1,_t);						    \
347
    umul_ppmm(p3,_t,m,n2);						    \
348
    __FP_FRAC_ADDI_2(p3,p2,_t);						    \
349
  } while (0)
350

351
/*
352
 * Division algorithms:
353
 */
354

355
#define _FP_DIV_MEAT_4_udiv(fs, R, X, Y)				    \
356
  do {									    \
357
    int _i;								    \
358
    _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m);				    \
359
    _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4);					    \
360
    if (_FP_FRAC_GT_4(X, Y))						    \
361
      {									    \
362
	_n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1);			    \
363
	_FP_FRAC_SRL_4(X, 1);						    \
364
      }									    \
365
    else								    \
366
      R##_e--;								    \
367
									    \
368
    /* Normalize, i.e. make the most significant bit of the 		    \
369
       denominator set. */						    \
370
    _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs);				    \
371
									    \
372
    for (_i = 3; ; _i--)						    \
373
      {									    \
374
        if (X##_f[3] == Y##_f[3])					    \
375
          {								    \
376
            /* This is a special case, not an optimization		    \
377
               (X##_f[3]/Y##_f[3] would not fit into UWtype).		    \
378
               As X## is guaranteed to be < Y,  R##_f[_i] can be either	    \
379
               (UWtype)-1 or (UWtype)-2.  */				    \
380
            R##_f[_i] = -1;						    \
381
            if (!_i)							    \
382
	      break;							    \
383
            __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0],	    \
384
			    Y##_f[2], Y##_f[1], Y##_f[0], 0,		    \
385
			    X##_f[2], X##_f[1], X##_f[0], _n_f[_i]);	    \
386
            _FP_FRAC_SUB_4(X, Y, X);					    \
387
            if (X##_f[3] > Y##_f[3])					    \
388
              {								    \
389
                R##_f[_i] = -2;						    \
390
                _FP_FRAC_ADD_4(X, Y, X);				    \
391
              }								    \
392
          }								    \
393
        else								    \
394
          {								    \
395
            udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]);  \
396
            umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0],		    \
397
			  R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]);	    \
398
            X##_f[2] = X##_f[1];					    \
399
            X##_f[1] = X##_f[0];					    \
400
            X##_f[0] = _n_f[_i];					    \
401
            if (_FP_FRAC_GT_4(_m, X))					    \
402
              {								    \
403
                R##_f[_i]--;						    \
404
                _FP_FRAC_ADD_4(X, Y, X);				    \
405
                if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X))	    \
406
                  {							    \
407
		    R##_f[_i]--;					    \
408
		    _FP_FRAC_ADD_4(X, Y, X);				    \
409
                  }							    \
410
              }								    \
411
            _FP_FRAC_DEC_4(X, _m);					    \
412
            if (!_i)							    \
413
	      {								    \
414
		if (!_FP_FRAC_EQ_4(X, _m))				    \
415
		  R##_f[0] |= _FP_WORK_STICKY;				    \
416
		break;							    \
417
	      }								    \
418
          }								    \
419
      }									    \
420
  } while (0)
421

422

423
/*
424
 * Square root algorithms:
425
 * We have just one right now, maybe Newton approximation
426
 * should be added for those machines where division is fast.
427
 */
428
 
429
#define _FP_SQRT_MEAT_4(R, S, T, X, q)				\
430
  do {								\
431
    while (q)							\
432
      {								\
433
	T##_f[3] = S##_f[3] + q;				\
434
	if (T##_f[3] <= X##_f[3])				\
435
	  {							\
436
	    S##_f[3] = T##_f[3] + q;				\
437
	    X##_f[3] -= T##_f[3];				\
438
	    R##_f[3] += q;					\
439
	  }							\
440
	_FP_FRAC_SLL_4(X, 1);					\
441
	q >>= 1;						\
442
      }								\
443
    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);			\
444
    while (q)							\
445
      {								\
446
	T##_f[2] = S##_f[2] + q;				\
447
	T##_f[3] = S##_f[3];					\
448
	if (T##_f[3] < X##_f[3] || 				\
449
	    (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2]))	\
450
	  {							\
451
	    S##_f[2] = T##_f[2] + q;				\
452
	    S##_f[3] += (T##_f[2] > S##_f[2]);			\
453
	    __FP_FRAC_DEC_2(X##_f[3], X##_f[2],			\
454
			    T##_f[3], T##_f[2]);		\
455
	    R##_f[2] += q;					\
456
	  }							\
457
	_FP_FRAC_SLL_4(X, 1);					\
458
	q >>= 1;						\
459
      }								\
460
    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);			\
461
    while (q)							\
462
      {								\
463
	T##_f[1] = S##_f[1] + q;				\
464
	T##_f[2] = S##_f[2];					\
465
	T##_f[3] = S##_f[3];					\
466
	if (T##_f[3] < X##_f[3] || 				\
467
	    (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] ||	\
468
	     (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1]))))	\
469
	  {							\
470
	    S##_f[1] = T##_f[1] + q;				\
471
	    S##_f[2] += (T##_f[1] > S##_f[1]);			\
472
	    S##_f[3] += (T##_f[2] > S##_f[2]);			\
473
	    __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1],	\
474
	    		    T##_f[3], T##_f[2], T##_f[1]);	\
475
	    R##_f[1] += q;					\
476
	  }							\
477
	_FP_FRAC_SLL_4(X, 1);					\
478
	q >>= 1;						\
479
      }								\
480
    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);			\
481
    while (q != _FP_WORK_ROUND)					\
482
      {								\
483
	T##_f[0] = S##_f[0] + q;				\
484
	T##_f[1] = S##_f[1];					\
485
	T##_f[2] = S##_f[2];					\
486
	T##_f[3] = S##_f[3];					\
487
	if (_FP_FRAC_GE_4(X,T))					\
488
	  {							\
489
	    S##_f[0] = T##_f[0] + q;				\
490
	    S##_f[1] += (T##_f[0] > S##_f[0]);			\
491
	    S##_f[2] += (T##_f[1] > S##_f[1]);			\
492
	    S##_f[3] += (T##_f[2] > S##_f[2]);			\
493
	    _FP_FRAC_DEC_4(X, T);				\
494
	    R##_f[0] += q;					\
495
	  }							\
496
	_FP_FRAC_SLL_4(X, 1);					\
497
	q >>= 1;						\
498
      }								\
499
    if (!_FP_FRAC_ZEROP_4(X))					\
500
      {								\
501
	if (_FP_FRAC_GT_4(X,S))					\
502
	  R##_f[0] |= _FP_WORK_ROUND;				\
503
	R##_f[0] |= _FP_WORK_STICKY;				\
504
      }								\
505
  } while (0)
506

507

508
/*
509
 * Internals 
510
 */
511

512
#define __FP_FRAC_SET_4(X,I3,I2,I1,I0)					\
513
  (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
514

515
#ifndef __FP_FRAC_ADD_3
516
#define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)		\
517
  do {								\
518
    int _c1, _c2;							\
519
    r0 = x0 + y0;						\
520
    _c1 = r0 < x0;						\
521
    r1 = x1 + y1;						\
522
    _c2 = r1 < x1;						\
523
    r1 += _c1;							\
524
    _c2 |= r1 < _c1;						\
525
    r2 = x2 + y2 + _c2;						\
526
  } while (0)
527
#endif
528

529
#ifndef __FP_FRAC_ADD_4
530
#define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)	\
531
  do {								\
532
    int _c1, _c2, _c3;						\
533
    r0 = x0 + y0;						\
534
    _c1 = r0 < x0;						\
535
    r1 = x1 + y1;						\
536
    _c2 = r1 < x1;						\
537
    r1 += _c1;							\
538
    _c2 |= r1 < _c1;						\
539
    r2 = x2 + y2;						\
540
    _c3 = r2 < x2;						\
541
    r2 += _c2;							\
542
    _c3 |= r2 < _c2;						\
543
    r3 = x3 + y3 + _c3;						\
544
  } while (0)
545
#endif
546

547
#ifndef __FP_FRAC_SUB_3
548
#define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0)		\
549
  do {								\
550
    int _c1, _c2;							\
551
    r0 = x0 - y0;						\
552
    _c1 = r0 > x0;						\
553
    r1 = x1 - y1;						\
554
    _c2 = r1 > x1;						\
555
    r1 -= _c1;							\
556
    _c2 |= r1 > _c1;						\
557
    r2 = x2 - y2 - _c2;						\
558
  } while (0)
559
#endif
560

561
#ifndef __FP_FRAC_SUB_4
562
#define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0)	\
563
  do {								\
564
    int _c1, _c2, _c3;						\
565
    r0 = x0 - y0;						\
566
    _c1 = r0 > x0;						\
567
    r1 = x1 - y1;						\
568
    _c2 = r1 > x1;						\
569
    r1 -= _c1;							\
570
    _c2 |= r1 > _c1;						\
571
    r2 = x2 - y2;						\
572
    _c3 = r2 > x2;						\
573
    r2 -= _c2;							\
574
    _c3 |= r2 > _c2;						\
575
    r3 = x3 - y3 - _c3;						\
576
  } while (0)
577
#endif
578

579
#ifndef __FP_FRAC_DEC_3
580
#define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0)				\
581
  do {									\
582
    UWtype _t0, _t1, _t2;						\
583
    _t0 = x0, _t1 = x1, _t2 = x2;					\
584
    __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0);		\
585
  } while (0)
586
#endif
587

588
#ifndef __FP_FRAC_DEC_4
589
#define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0)			\
590
  do {									\
591
    UWtype _t0, _t1, _t2, _t3;						\
592
    _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3;				\
593
    __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0);		\
594
  } while (0)
595
#endif
596

597
#ifndef __FP_FRAC_ADDI_4
598
#define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i)					\
599
  do {									\
600
    UWtype _t;								\
601
    _t = ((x0 += i) < i);						\
602
    x1 += _t; _t = (x1 < _t);						\
603
    x2 += _t; _t = (x2 < _t);						\
604
    x3 += _t;								\
605
  } while (0)
606
#endif
607

608
/* Convert FP values between word sizes. This appears to be more
609
 * complicated than I'd have expected it to be, so these might be
610
 * wrong... These macros are in any case somewhat bogus because they
611
 * use information about what various FRAC_n variables look like 
612
 * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
613
 * the ones in op-2.h and op-1.h. 
614
 */
615
#define _FP_FRAC_CONV_1_4(dfs, sfs, D, S)				\
616
   do {									\
617
     if (S##_c != FP_CLS_NAN)						\
618
       _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),	\
619
			  _FP_WFRACBITS_##sfs);				\
620
     else								\
621
       _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));	\
622
     D##_f = S##_f[0];							\
623
  } while (0)
624

625
#define _FP_FRAC_CONV_2_4(dfs, sfs, D, S)				\
626
   do {									\
627
     if (S##_c != FP_CLS_NAN)						\
628
       _FP_FRAC_SRS_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),	\
629
		      _FP_WFRACBITS_##sfs);				\
630
     else								\
631
       _FP_FRAC_SRL_4(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));	\
632
     D##_f0 = S##_f[0];							\
633
     D##_f1 = S##_f[1];							\
634
  } while (0)
635

636
/* Assembly/disassembly for converting to/from integral types.  
637
 * No shifting or overflow handled here.
638
 */
639
/* Put the FP value X into r, which is an integer of size rsize. */
640
#define _FP_FRAC_ASSEMBLE_4(r, X, rsize)				\
641
  do {									\
642
    if (rsize <= _FP_W_TYPE_SIZE)					\
643
      r = X##_f[0];							\
644
    else if (rsize <= 2*_FP_W_TYPE_SIZE)				\
645
    {									\
646
      r = X##_f[1];							\
647
      r <<= _FP_W_TYPE_SIZE;						\
648
      r += X##_f[0];							\
649
    }									\
650
    else								\
651
    {									\
652
      /* I'm feeling lazy so we deal with int == 3words (implausible)*/	\
653
      /* and int == 4words as a single case.			 */	\
654
      r = X##_f[3];							\
655
      r <<= _FP_W_TYPE_SIZE;						\
656
      r += X##_f[2];							\
657
      r <<= _FP_W_TYPE_SIZE;						\
658
      r += X##_f[1];							\
659
      r <<= _FP_W_TYPE_SIZE;						\
660
      r += X##_f[0];							\
661
    }									\
662
  } while (0)
663

664
/* "No disassemble Number Five!" */
665
/* move an integer of size rsize into X's fractional part. We rely on
666
 * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
667
 * having to mask the values we store into it.
668
 */
669
#define _FP_FRAC_DISASSEMBLE_4(X, r, rsize)				\
670
  do {									\
671
    X##_f[0] = r;							\
672
    X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE);	\
673
    X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \
674
    X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \
675
  } while (0)
676

677
#define _FP_FRAC_CONV_4_1(dfs, sfs, D, S)				\
678
   do {									\
679
     D##_f[0] = S##_f;							\
680
     D##_f[1] = D##_f[2] = D##_f[3] = 0;				\
681
     _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));	\
682
   } while (0)
683

684
#define _FP_FRAC_CONV_4_2(dfs, sfs, D, S)				\
685
   do {									\
686
     D##_f[0] = S##_f0;							\
687
     D##_f[1] = S##_f1;							\
688
     D##_f[2] = D##_f[3] = 0;						\
689
     _FP_FRAC_SLL_4(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));	\
690
   } while (0)
691

692
#endif
693

694
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